Selected Works of
Professor Herbert Kroemer
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Selected Works of Professor Herbert Kroemer
Editor
C K Maiti Indian Institute of Technology, Kharagpur, India
World scientific N E W JERSEY
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CHENNAI
Published by
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British Library Cataloguing-in-PublicationData A catalogue record for this book is available from the British Library.
SELECTED WORKS OF PROFESSOR HERBERT KROEMER Copyright 0 2008 by World Scientific Publishing Co. Re. Ltd. All rights reserved. This book, or parts thereoL may not be reproduced in any form or by any means. electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher.
For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher.
ISBN- 13 978-9 81-270-901-1 ISBN-10981-270-901-0
Printed in Singapore by World Scientific Printers
Contents
1. Introduction
1
2. The Untold Story
11
3. Biography of Herbert Kroemer
15
4. The Nobel Lecture
22
5. Publications List
43
6. Herbert Kroemer: Oral History
75
7 . Not Just the Blue Sky
99
8. Reprinted Articles 8.1 General Principles of Heterostructures and HBTs 8.2 Hot-Electron Negative Resistance Effects 8.3 GaAs and GaP on Si and Related Topics 8.4 Superconductor-Semiconductor Hybrids
105
9. Herbert Kroemer on Nanotechnology
370
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Introduction 1
Introduction
Introduction 3
Kroemer was born in Germany in 1928 in Weimar, Germany, and studied at the Universities of Jena and Goettingen. Kroemer received his doctorate in theoretical physics in 1952 from the University of Goettingen, Niedersachen, Germany with a dissertation on hot-electron effects in transistors, setting the stage for a career in research on the physics of semiconductors and semiconductor devices. He began wondering why the emerging junction transistors were so slow compared to the earlier point contact transistors. This led him to ask the key question: ' .how can an electric field be built into the base region of a junction transistor?" After his doctorate, he joined the Central Bureau of Telecommunications Technology of the German Postal Service, where he made a pioneering contribution to the then emerging field of solid-state transistors by inventing the drift transistor. He worked in a number of research laboratories in Germany before coming to the U.S. in 1954 where he continued working in heterostructures. Kroemer figured one possible way to speed up transistors, not using a single semiconductor, but a graded base region that started with one material and ended up in another material with a continuous transition between them. Associated with this gradient should then be a force that pushes the charge carriers from the emitter to the collector. Kroemer referred to these new kinds of forces as . 'quasi-electric" fields. His first paper on drift transistor introduced the concept of a doping-engineered electric field in the base to reduce the base transit time. The paper predicted a 8-fold increase in the theoretical frequency limit as compared to Shockley5 . .diffusion'' bipolar transistors. The concept of aiding base transport with a builtin electric field resulting from the variation of base doping density is in use in virtually all bipolar transistors fabricated today, and is one of the central concepts in BJT design. Kroemer expanded his concepts into a new general device design principle going far beyond the starting point of speeding up the bipolar transistors: composition gradient to act as a force on the electrons, that might make possible new devices fundamentally impossible without the new force. These concepts became the backbone of heterostructure bipolar transistor (HBT) technology, even invading silicon technology. An extension of the concept is the basis for much of the speed advantage of present Silicon-Germanium (SiGe) HBTs (see Figure 2). The rf telecommunication industry has built up around the devices Kroemer envisioned in the early years. This 1954 paper introduced a host of far-reaching ideas and an English translation of a portion of this paper is included in this Volume. His landmark 1957 paper in the RCA Review, entitled . .Quasi-Electric and Quasi-Magnetic Fields in Nonuniform Semiconductors" explained how transistor performance could be improved by the incorporation of quasi-electric fields. The fact that semiconductors can emit light in response to electric currents has been recognized since the early 1930s. However, it took two decades before this phenomenon could be understood to be due to electron-hole recombination at the interfaces. Also the advent of Ill-V compound seniiconductors altered this situation during the early 1960s. In 1959, Kroemer moved to Central Research Labs at Varian Associates, where he invented the semiconductor heterostructure laser in 1963, which was a straightforward application of the same principle of heterojunctions he worked with and could operate continuously at room temperature. Kroemer was the first to realize the possibilities for carrier and photon confinement offered by a double heterostructure, at a time when the intense research on homojunction semiconductor light emitters seemed to be making little progress. Kroemer suggested that a vastly improved laser could be designed by sandwiching a layer of a narrow band gap semiconductor between two wide band gap semiconductors in another landmark paper in the Proceedings of the IEEE in 1963, a paper that drew little attention at the time.
4
Selected Works of Professor Herbert Kroemer
S.31idcrdntdr aUS
ARCHIV DER ELEKTRISCHEN UBERTRAGUNG
Zur Theorie des Diffusions- und des Drifttransistors 111. Dimensionierungsfragen Von
HERBERTKR&MXR*
SIitteilung aus dem Fernmeldehchnischen Zentrdamt Rarrnetadt (A.
E.If.8 [1954],499-5iN;
efngegnngfm am 24,Yull 1954)
.I..
AuBer durch inhomogene Hotierung emes homo. genen Halbleiters lriBt sich ein Driftfeld such dadurch erzeugen, dal3 man die Breite des verbotenen Bandes selbst andert, indem man die Basiszone aus einem nichtvtijchiometrischen -V)]-'" (6 a) Mischkristalf verschiedener Halb. leiter mit verschiedenen Bandab&&Saden(z. B. Ge.Si) heratellt, deassn Zusarnmensetzung sich innerhalb der Basis atetig iindert. Bei nichf zu hoher Dotierung bbiben dann die Emitterkapazitiitsn klein, obwohl selbst dann, wem diese Dotierung konstant ist, ein Driftpotential yon
.
Eo,E--Ea,c (1 h ) erzeugber ware. Xit Ge-Si gkbe dss etwa 0,4eV= 16 kT. ? h i $ ;r Q $ L a d Eine Varimte dieses Verfahrens besteht da in, m a r in der Basiszone den honiogenen Halbleiter mit inhomogener Dotierung beizubehalten, fur die Emitterzone jedoch einen Halbleiter mit wesentlich groBerem Bandabstand zu wiihlen2. Dsnn ist es nlimlich miiglich, die StiirvtelIenkonzentmtionP,irn Emitter weit unter N, zu senken, ohne daB der Wirku ngsgmd des E m i t t m sbnirnmt. Dadurcch nehmen aber gemiiI3 Gl. (88) auch die ecbten Kapazitiiten ab, und unter Urnstiinden kann AV noch fiber die AV
(a S - 6 2
9
-
Den Hinweis hietsuf verdanke ich Herrn A. H . i i n ~ i l i ; aiehe hiertu auch LEXOVEC[3].
The start of SiGe heterostructures: portion of a page from reference: H. Kroemer, . ' Zur Theorie des Diffusions- und des Drifttransistors: 111. Dimensionierungs-fragen,"Archiv. d. Elektrischen Ubertragung, Vol. 8, pp. 499-504, 1954. Source: C. K. Maiti.
Introduction 5
Although he proposed the idea of the double-heterostructure laser (DHL), he was refused resources to develop the necessary technology, on the grounds that this device could not possibly compete with existing lasers. Interestingly, this novel idea is the basis for the entire modern optoelectronics industry. In fact, these ideas were far ahead of their time, and required the development of modern epitaxial growth technology before they could become mainstream technologies. Not only lasers, but also light emitting diodes (LEDs), such as the blue and green and white LEDs, use the double heterostructure design principle Kroemer envisioned back in 1963. The DHL created its own applications, from the CD player to fiber communications, without which there could never have been an Internet. Gunn effect was discovered in the early 1960s. Not being able t o work on the laser, Kroemer pursued the problem of high-field electron transport, especially negative-resistance effects such as the Gunn effect, and the crucial enabling role of non-trivial energy band structure in such devices. He became the first researcher to explain Gunn effect fully in 1964. He joined the faculty of the University of Colorado in 1968 and moved t o UCSB in 1976 where he turned to experimental work and became one of the early pioneers in molecular beam epitaxy, concentrating on applying the technology to new materials systems, such as GaP and GaAs on silicon. 1980s became a decade of * 'Heterostructures for Everything'' - a topic that still continues to dominate not only the Ill-V compound semiconductors but integrated circuits involving the mainstream silicon technology. Kroemer has addressed the understanding of heterojunctions and heterointerfaces with his theoretical prediction of band line-ups and the problems associated with connecting electronic wave functions across heterointerfaces. Kroemer realized that a pure I n k channel may offer the possibility of a very fast electron with the added advantage of excellent confinement offered by AlSb barriers. Thus, in the mid-eighties, his work shifted towards the * -6.1 A group" of materials including InAs, GaSb, and AISb. Kroemer is best described by his favorite talk: . ' Heterostructures for Everything.'' Kroemer's career is a fine example of deep, fundamental scientific work having a profound effect on technology and society. He is credited with being the pioneer in the field of heterostructure electronics, which now includes quantum well heterostructures and superlattices. This area involves electron transport in semiconductor superlattices under sufficiently strong electric fields that the electrons undergo oscillations within the tilted energy bands. Such structures might be capable of serving as oscillators - commonly called Bloch oscillators - up to frequencies in the terahertz regime. Today Kroemer continues his interest with new research areas, like electromagnetic wave propagation in photonic crystals, especially negative-refraction effects, as well as dissimilar materials through his investigations of so-called broken-bandgap combinations of arsenides and antimonides having mid-infrared device applications, and the induced superconducting behavior of semiconductors sandwiched between superconductors. His recent work involves superconductor semiconductor hybrid structures where Ink-AISb quantum wells are contacted by superconducting niobium electrodes, which induce superconductivity in the semiconductor. Alan J. Heeger, Alan G. MacDiarmid, and Hideki Shirakawa were awarded 2000 Nobel prize for Chemistry ..for the discovery and development of conductive polymers,'' a revolutionary discovery that plastics can have the properties of metals and semiconductors, a finding that created an important new field of research. There is a great deal of commonality between Heeger and Kroemer, particularly in the conducting and semiconducting materials field and between chemistry and physics, as is evidenced from two joint publications of Heeger and Kroemer.
6 Selected Works of Professor Herbert Kroemer
Kroemer is a Fellow of the IEEE and the American Physical Society, and a Foreign Associate of the U.S. National Academy of Engineering. He has received numerous awards, including the IEEE Medal of Honor, EDS J. J. Ebers and Jack A. Morton Awards, the Heinrich Welker Medal, and the Alexander von Humboldt Research award. He holds honorary doctorates from the Technical University of Aachen, Germany; the University of Lund, Sweden; and from the University of Colorado. He received Germany's Bundesverdienstkreuz (Order of Merit), the highest award given by the Federal Republic of Germany. A German citizen, Kroemer was elected as a foreign associate of the NAS. He even has an asteroid named for him when the German astronomer who discovered it learned of Kroemer's distinguished career. Kroemer's impact in education has also been significant, with two unique and widely used text books; Thermal Physics by Kittel and Kroemer and Quantum Mechanics. Kroemer has always preferred to work on problems that are one or two generation ahead of established mainstream technology. I t will take years to fully exploit his more recent innovations and ideas. A theoretician, Kroemer is not bothered that he has not profited personally from the practical applications of his lifetime research. His publications may be classified, in general, in the following areas: general principles of heterostructures and HBTs, hot-electron negative resistance effects, GaAs and GaP on Si and related topics, and superconductor-semiconductor hybrids. Some of his important publications reprinted in this volume are listed below. The Volume starts with Kroemer's autobiography and followed by the Nobel lecture. The next two articles on Herbert Kroemer are the ' 'Oral History from the IEEE" and "Not Just Blue Sky" from IEEE Spectrum focus on various aspects, such as his early days and Kroemer 'himself' to prevailing political and social conditions in postwar Germany. These two articles are expected to be of special interest to Science historians. The next 35 articles have been selected mainly from the considerations of technical importance and are arranged area wise chronologically.
-
Introduction 7
Technical Articles Reprinted in this Volume
8 Selected Works of Professor Herbert Kroemer
H. Kroemer, .Zur Theorie des Germaniumgleichrichters und des Transistors," Zeitschr. f. Phys., Vol. 134, pp. 435-450, 1953. H. Kroemer, . 'Theory of a Wide-Cap Emitter for Transistors," Proc. IRE, Vol. 45(1 I), pp. 1535-1 537, 1957.
H. Kroemer,
*
' A Proposed Class of Heterojunction Injection Lasers," Proc. IEEE, Vol. 5 1 (1 2),
pp. 1782-1 783, Dec. 1963. [Discussion ibid., Vol. 52(4), pp. 426-427, 19641.
H. Kroemer, . .Heterostructures for Everything: Device Principle of the 1980's?" Japan. J. Appl. Phys., Vol. 20 (SUPPI. l), pp. 9-13, 1981. H. Kroemer, ' Heterostructure Bipolar Transistors and Integrated Circuits," Proc. IEEE, Vol. 70( 1 ), pp. 13-25, 1982. .L
H. Kroemer and C . Griffiths, . ' Staggered-Lineup Heterojunctions as Sources of Tunable BelowGap Radiation: Operating Principle and Semiconductor Selection," IEEE Electron Dev. Lett., Vol. EDL-4(1), pp. 20-22, 1983. Rebuttal to Response to . 'Critique to Two Recent Theories of Heterojunction Lineups,'' IEEE Electron Dev. Lett., Vol. EDL-4( lo), p. 365, 1983. H. Kroemer, ' Heterostructure Bipolar Transistors: What Should We Build?" J. Vac. Sci. Technol. B, Vol. 1 (2), pp. 126-1 30, 1983. H. Kroemer, . .Heterostructure Devices: A Device Physicist Looks at Interfaces," Surf. Sci., Vol. 132, pp. 543-576, 1983.
H. Kroemer, . .Barrier Control and Measurements: Abrupt Semiconductor Heterojunctions," J. Vac. Sci. Technol. B, Vol. 2(3), pp. 433-439, 1984. H. Kroemer and H. Okamoto, * .Some Design Considerations for Multi-Quantum-Well Lasers," Japan. J. Appl. Phys., Vol. 23, pp. 970-974, 1984. E. J. Caine, S. Subbanna, H. Kroemer, J. L. Merz, and A. Y. Cho, . ' Staggered-Lineup Heterojunctions as Sources of Tunable Below-Cap Radiation: Experimental Verification," Appl. Phys. Lett., Vol. 45(10), pp. 1 123-1 125, 1984. M. J. Mondry and H. Kroemer, . .Heterojunction Bipolar Transistor Using a (Ca,ln)P Emitter on a GaAs Base, Grown by Molecular Beam Epitaxy," IEEE Elect. Dev. Lett, Vol. EDL-6(4), pp. 175-177, 1985.
D. I. Babic and H. Kroemer, . 'The Role of Nonuniform Dielectric Permittivity in the Determination of Heterojunction Band Offsets by C-V Profiling Through lsotype Heterojunctions," Solid-state Electron., Vol. 28( lo), pp. 101 5-1 01 7, 1985. H. Kroemer, . .Band Offsets at Heterointerfaces: Theoretical Basis, and Review of Recent Experimental Work," Surf. Sci., Vol. 174, pp. 299-306, 1986. M. A. Rao, E. J. Caine, S. 1. Long, and H. Kroemer, . 'An (AI,Ga)As/GaAs heterostructure bipolar transistor with non-alloyed graded-gap contacts to the base and emitter,'' IEEE Electron Dev. Lett. EDL-8(1), pp. 30-32, 1987.
Introduction 9 G. Tuttle, H. Kroemer, and J. H. English, * .Electron concentrations and mobilities in AISb/lnAs/AISb quantum wells," J. Appl. Phys., Vol. 65(12), pp. 5239-5242, 1989.
P. F. Hopkins, A. J. Rimberg, R. M. Westervelt, G. Tuttle, and H. Kroemer, . *Quantum Hall effect in InAs/AISb quantum wells," Appl. Phys. Lett., Vol. 58(13), pp. 1428-1430, 1991. 1. Sela, D. E. Watkins, B. K. Laurich, D. L. Smith, S. Subbanna, and H. Kroemer, . 'Modulated photoabsorption in strained Gal -xlnxAs/GaAs multiple quantum wells," Phys. Rev. B, Vol. 43(14), pp. 1 1 884-11892, 1991. S. A. Chalmers, H. Kroemer, and A. C. Gossard, . 'The growth of (AI,Ga)Sb tilted superlattices and their heteroepitaxy with lnAs to form corrugated-barrier quantum wells,'' J. Cryst. Growth, Vol. 1 1 1, pp. 647-650,1991.
H. Kroemer, C. Nguyen, and B. Brar, . 'Are there Tamm-state donors at the InAs-AISb quantum well interface?" J. Vac. Sci. Technol. B, Vol. 10(4), pp. 1769-1772, 1992.
B. Brar, H. Kroemer, and J. H. English, ' "Quasi-direct' narrow GaSb/AISb (100)quantum wells," J.Cryst. Growth, Vol. 127, pp. 752-754,1993. H. Kroemer, * Semiconductor Heterojunctions at the Conference on the Physics and Chemistry of Semiconductor Interfaces: A Device Physicists Perspective," J. Vac. Sci. Technol. B, Vol. 1 1 (4), pp. 1354-1361, 1993.
.
H. Kroemer,
'
Proposed Negative-Mass Microwave Amplifier," Phys. Rev., Vol. 109(5), p.
1856, 1958. H. Kroemer,
H. Kroemer, 56, 1968.
. 'Theory of the Gunn Effect," Proc. IEEE, Vol. 52(12), p. 1736, 1964. . 'Negative Conductance in Semiconductors," IEEE Spectrum, Vol. 5(1), pp. 47-
H. Kroemer, * Generalized Proof of Shockley's Positive Conductance Theorem,'' Proc. IEEE, Vol. 58( 1 I), pp. 1844-1845, Nov. 1970. [Comments on ' *Generalized Proof of Shockleys Positive Conductance Theorem", Proc. IEEE, Vol. 59(8), pp. 1282-1283, 19711.
H. Kroemer, . * Hot-Electron Relaxation Effects in Devices," Solid-state Electron., Vol. 2 1 (1 ), pp. 61 -67,1978. H. Kroemer,
*
.Polar-on-Nonpolar Epitaxy,"
J. Cryst. Growth, Vol. 81, pp. 193-204,1987.
T.-Y. Liu, P. M. Petroff, and H. Kroemer, ' ' Luminescence of GaAs/(AI,Ga)As superlattices grown on Si substrates, containing a high density of threading dislocations: Strong effect of the superlattice period," J. Appl. Phys., Vol. 64(12), pp. 6810-6814, 1988.
. 'GaAs on Si, and Related Systems: Problems and Prospects," J. Cryst. Growth, Vol. 95, pp. 96-102,1989.
H. Kroemer, T.-Y. Liu, and P. M. Petroff,
H. Kroemer, C. Nguyen, and E. L. Hu, . .Electronic Interactions at SuperconductorSemiconductor Interfaces," Solid-state Electron., Vol. 37(4-6), pp. 1021 -1 025, 1994.
10 Selected Works of Professor Herbert Kroemer
H. Kroemer, . .Superconductor-Semiconductor Devices,'' NATO Adv. Res. Workshop Future Trends in Microelectronics: Reflections on the Road to Nanotechnology, Ile de Bendor, France, S. Luryi, J. Xu, and A. Zaslavsky, Eds., NATO AS1 Series: Series E: Applied Sciences, Vol. 323, Kluwer Academic Publishers, pp. 237-250, 1996.
P. M Petroff, K. Ensslin, M. S. Miller, S. A. Chalmers, H. Weman, J. L. Merz, H. Kroemer, and A. C. Cossard, . 'Novel Approaches in 2 and 3 Dimensional Confinement Structures: Processing and Properties,'' Superlattices and Microstructures, Vol. 8(1), pp. 35-39, 1990. H. Kroemer, * ' Heterostructures Tomorrow: From Physics to Moore's Law," Inst. Phys. Conf. Ser., Vol. 166, pp. 1-1 1, 1999. H. Kroemer, 2003,
.Speculations about Future Directions,''
J. Cryst. Growth, Vol. 25 1, pp. 1 7-22,
The Untold Story 11
The start of SiGe heterostructures: portion of a page from reference: H. Kroemer, Zur Theorie des Diffusions- und des Drifttransistors: HI. Dimensionierungs-fragen, ' ' Archiv d. Elektrischen U bertragung, VOI, 8, pp. 499-504, 1954.
..
AuBer durch inhomogene Dotierung eines homogenen Halbleiters lafit sich ein Driftfeld auch dadurch erzeugen, da13 man die Breite des verbotenen Bandes selbst andert, indem man die Basiszone aus einem nichtstochiometrischen Mischkristall verscheidener Halbleiter mit verschiedenen Bandabstanden (z. B. Ge-Si) herstellt, dessen Zusammensetzung sich innerhalb der Basis stetig andert. Bei nicht zu hoher Dotierung bleiben dann die Emitterkapazitaten klein, obwohl selbst dann, wenn diese Dotierung konstant ist, ein Driftpotential von Av= EB,E- EB,C .
(W
erreichbar ware. Mit Ge-Si gabe das etwa 0.4 eV = 16 hT.
Besides by inhomogeneous doping of a homogeneous semiconductor, a drift field may also be generated through varying the energy gap itself, by making the base region from a nonstoichiometric mixed crystal of different semiconductors with different energy gaps (for example, Ge-Si), the composition of which varies continuously through the base. If the doping is not too high, the emitter capacitances then remain small, although even if the doping is constant, a drift potential of
could be obtained. With Ge-Si this would yield about 0.4 eV = 16 kT.
Eine Variante dieses Verfahrens besteht darin, zwar in der Basiszone den homogenen Halbleiter mit inhomogener Dotierung beizubehalten, fur die Emitterzone jedoch einen Halbleit er mit we sentlich groner e m Bandabstand zu wahlen.2 Denn ist es namlich moglich, die Storstellenkonzentration Pe im Emitter weit unter Na zu senken, ohne daB der Wirkungsgrad des Emitters abnimmt. Dadurch nehmen aber gemal3 G1. (6a) auch die echten Kapazitaten ab, und unter Umstanden kann AV noch uber die durch Gl. (la) gegebene Grenze erhoht werden. ....
A variation of this procedure would consist of retaining, within the basis zone, the homogeneous semiconductor with a n inhomogeneous doping, but to select for the emitter zone a semiconductor with a significantly larger energy gap? For then it becomes possible to lower the doping concentration P, far below N, [i.e, the donor concentration in the base on the emitter side] without a decrease in the emitter efficiency. But in this way, acording to (6a), the true capacitances also decrease, and AV may potentially be increased even beyond the limit given by (la). .... I owe this suggestion t o Mr. A. Hahnlein;
2 Den Hinweis hierauf verdanke ich Herrn
A. Hahnlein; siehe hierzu auch Lehoved [ 3 ] .
see also Lehovec [3] on this matter.
Wir behandeln diese Moglichkeiten in vorliegender Arbeit nicht naher, da uber die physikalischen und technologischen Eigenschaften von Halbleiter-Mischphasen aul3er einer Arbeit von Busch und Winkler [5] hierzu noch keine brauchbaren Untersuchungen vorliegen.
We do not treat these possibilities in the present paper any further, because there are no usable investigations about the physical and technological properties of semiconductor mixed phases, besides a paper by Busch and Winkler [5].
Comment: B&W studied the properties of the semiconductor alloy system Mg2(GexSi1-4 *
Biography of Herbert Kroemer 15
H. Kroemer, "Quasi-Electric Fields and Band Offsets: Teaching Electrons New Tricks," Les Prix Nobel, The Nobel Prizes 2000, The Nobel Foundation, Stockholm, pp. 101-121 (Biography on pp. 95-loo), 2001. Copyright The Nobel Foundation 2000.
16 Selected Works of Professor Herbert Kroemer
Herbert Kroemer Autobiography I was born on August, 25, 1928 in Weimar, Germany. My father was a civil servant working for the city administration of my home town; my mother was a classical German “Haiisfraii.” Both came from simple skilled-craftsmen families. Neither had a high-school education, but there was never any doubt that they wanted t o have their children obtain the best education they could afford. My mother, in particular, pushed relentlessly for top performance in school: simply doing well was not enough. Fortunately, I breezed through 12 years of school almost, effortlessly, not, once requiring help with homework from my parents. Despite their insistence on excellence, my parents never pushed me in any particular academic direction; I was completely free to follow my inclinations, which ran towards math, physics, arid chemistry. When I finally told my parents that I wanted to study physics, my father merely wondered what that is, arid whether I could make a living with it,. I certainly could become a physics teacher at, a High School, or “Gymnasium,” a t,horoughly respectable profession. I did have one major problem in school, though: Discipline! I was often bored, arid entertained myself in various disruptive ways. A frequent punishment was an entry into the “Klassenbuch,” the daily class ledger. These entries were considered a very serious matter, arid if I had riot, been excellent academically, I would have risked being expelled. O~ice,after I had again been entered as having disturbed the class, the teacher who had overall responsibility for the class - Dr. Edith Richter, whom I adored - asked me in great exasperation: “Why again?” I told her that, I had been bored, whereupon she exploded: “Mr. Kroemer, one of the purposes of a higher education is that you learn to be bored gracefully.” I will never forget t,hat, outburst, - nor have I ever really learned t o be bored gracefully. Another teacher - Willibald Wimmer - had his own clever way of handling me. Before the end of the war, he had been an instructor at a local engineering college, ending up teaching math arid physics at our high school. He was used to dealing with more mature staderits, arid he treated iis as adults. I was way ahead of the curriculiim in math, and kept sliowing off. Worse, I taught some of my classmates math %ricks,” that were riot part, of the curriculum. So, Mr. Wimmer made a “treaty” wit’h me: While he could not excuse me from attending class, I was guaranteed a top grade without being required to turn in the homework assignments, and was permitted to do whatever I wanted t,o do during the hour, provided I kept absolutely quiet, - except when explicitly asked t,o speak up. Bot,h of us kept, that, treaty. Mr. Wimmer also became our physics teacher, a subject about which lie clearly knew little more than what was in the textbook. Realizing that I was deeply
Biography of Herbert Kroemer 17
into physics, he simply enlisted me and one other student to help him in lecture preparations, like setting up what apparatus had survived the war. Once I even was asked t o present the lecture myself, with him sitting in the front row and enjoying the show. It was a wonderful experience. Having graduated from the gymnasium in 1947, 1 was accepted as a physics student at the University of Jena, where I fell under the spell of the great Friedrich Hund, the most, brilliant lecturer I ever encountered. The joy did not last long. 111 early 1948 the political suppression in East, Germany became very severe, especially at rebellious universities like Jena. Every week, some of my fellow students had suddenly disappeared, and you never knew whether t,hey had fled t o the West, or had ended up in the German branch of Stalin’s Gulag, like the uranium mines near the Czech border. During the Berlin airlift,, I was in Berlin as a summer student, at the Siemens company, and I decided to go West via one of the empty airlift, return flights. From Berlin, I had wr t o several west German universities for admission, including Gottingen, bnt ot receive a reply before leaving Berlin (they had turned me down). I followed the advice of one of my Jena professors “why don’t you give my greetings t o Professor Konig in Gottingen.” Konig told me that, physics admissions were closed, but he passed me on for what was ost,ensibly just a friendly chat t o Professor Richard Becker and his alter-ego assistant, Dr. Gnther Leibfried. They in turn passed me 011 to Wolfgang Paul (Nobel 1989), and I think also to Robert Pohl. It soon dawned on me that this was not just a friendly social chat with people who had nothing b r to do, but a thorough examination. I remember one of the questions Paul asked me: “You know that, a mirror interchanges left, and right? - Then why doesn’t it interchange top and bottom?” In the end, I was returned t o Becker, who told me that two of the students who had been admitted were not coming, and a meeting was scheduled for the next day to select, who would get, the two openings. A few days later I received a postcard that, I had been accepted. Post-war Gottingen. was - intellectually - a wonderfully stimulating place. I was attracted t o one of the younger instructors - “Privatdozent” Dr. Hellwege - who offered a so-called Proseminar, where pre-research students would present, papers assigned t o them, and I participated in this for several semesters in a row. Once, the famous Fritz Houtermans visited Hellwege, and sat in on several of the presentations, including mine. I presented someone’s data that, yielded a reasonable straight line on a double-log plot,, and proudly claimed a power law for the data. Houtermans was not impressed: “On a double-log plot, my grandmother fits on a straight line.” I keep quoting Houtermans’ grandmother to my own students. Eventually, I signed up with Hellwege for a Diploma Thesis, which would probably have led to an experimental study of the optical spectra of some rare-earth salts. But Hellwege had a long waiting list, and in the meantime, Professor Fritz Sauter - a refugee who had found a temporary home as a guest in Becker’s Institute for Theoretical Physics - offered me a theoretical Diploma Thesis, based on a talk t,hat, I had given in one of his seminars. Hellwege suggested that I accept Sauter’s
18 Selected Works of Professor Herbert Kroemer
offer: “You will be finished with him before you can start with me.” So I became a theorist. The diploma thesis was an extension of a 1939 paper by Shockley on the nature of surface states in one-dimensional potentials. As one of the elaborations, I looked at the interface between two different periodic potentials, which confronted me for the first time with what we would today call the band offsets at heterojunctions. There was another early encounter with heterojunctions while working under Sauter. We made a field trip to the AEG research laboratories in Belecke, a small town in Westphalia. There, a DI. Poganski gave a beautiful demonstration that t,he selenium rectifier was not a Schottky barrier, but a p-n junction between ptype selenium and n-type CdSe, a true heterojunction - although that term did not exist yet. This must have had an at least sub-conscious influence on me: when I later started thinking about heterojunctions in earnest, the question whether such things could actually exist as real devices had an obvious answer: Of course! While working on my diploma, I gave another colloquium talk under Sauter, reporting on the famous Bardeen/Brattain paper “Physical Principles Involved in Transistor Action” (or some title like that). At the end I made some suggestion about some open questions raised by the authors. Sauter was intrigued and suggested that, as a possible Ph.D. topic. Sometime later, he came into my office and told me to stop further work on my Diploma thesis, and to simply write up what I had done so far.. When I protested, he insisted that>it, was time t o move on to the real thing, the Ph.D. dissertation. I had thus come into contact with one of Sauter’s strong beliefs, apparently dating back t o the tradition of the 20s: that degrees should not be awarded on the basis of having “served time,” but were basically certificates that t,he recipient, had proven capable of executing creative work independently, and no longer required supervision. In fact,, he clearly preferred quick dissertations. As a result, I received my Ph.D. before my 24th birthday, fast even for a theorist: Wonderful! The P1i.D. dissertation involved what we would today call hot-electron effects, in the collector space-charge layer of the then-new transistor. The idea was simple. Almost nothing was known about, the energy band structure of Ge, but someone’s theoretical estimates suggested - quite incorrectly - very narrow bands, especially for the valence band. In this case, if the field was strong enough, any holes in the valence might undergo what we now call Bloch oscillations. A few lines of algebra suggested that, for a given current density, the traveling hole concentration would increase with increasing field ( “Staueffekt~” ) , leading to strong space charge effects. The influence of t,hese space charges on the current-voltage characteristics of point, contactJ diodes and transistors formed the main body of the dissertation. My algebra also implied a decrease of electron drift velocity with increasing field, implying a negative differential conductivity. Knowing nothing about, electrical circuit theory, I was unaware how useful such a phenomenon could be, until Shockley pointed it out to me in a personal discussion two years later. But it became clear soon that my dissertation was unrelated t o reality. My assumptions about the band structure and about an energy-independent mean free
Biography of Herbert Kroemer 19
path had been invalid, and after the discovery of avalanclie breakdown it became obvious that the huge fields required for Bloch oscillations in a bulk semiconductor could never be reached. Twenty years later, after the pathbreaking work of Esaki and Tsu on negative differential conductivity in superlattices, I realized that I had in fact, anticipated their basic physics, albeit in a more primitive form: What, was notJ possible in bulk semiconductors, appeared to become possible in superlattices with their much longer period. Back to Sauter. He was not interested in closely supervising his students; he simply watched what they were doing on their own initiative. Still, he had a tremendous influence on me in mat,ters of methodology. Whenever I came to him with a pure physics idea, he would invariably say, with slight sarcasm: “But, Mr. Kroemer, you ought to be able to formulate this mathematically! ” If I came to him with a math formulation, I would get, in a similar tone: “But Mr. Kroemer, that is just math, what is the physics?” After a few encounters of this kind, you got the idea: You had to be able to go back and forth with ease. Yet, in t,he last, analysis, concepts took priority over formalism, the latter was simply an (indispensable) means to an end. This set of priorities clearly showed, and it had a profound influence on me. As a student of Sommerfeld, Santer was a superb mathematician himself. But he detested it when people were showing off their math skills by using math that was more advanced than necessary for the problem at hand. To the contrary: You were expected to show how simple you could make it. Because he was a great expertJ on Bessel functions, I once felt compelled to put, into the draft of my dissertation, an ad-hoc problem that required Bessel functions. He was not amused: “This has no business here; you just, put, it in to impress me. Take it, out>!” Richard Becker had exactly the same attitude (the two were close friends), arid I later encountered it again in Shockley. Under influences such as these, I never developed into a “hard-core Theorist, with a capital T,” but became basically a conceptualist who remained acutely aware of his limitations as a formalist, and whose personal role model was Niels Bohr more than anybody else amongst the Greats of Physics. The German 1952 job market for theoretical physicists was all but, nonexistent. New university positions were not created, and there were plenty of more senior people waiting to occupy any vacancies that might, open up. So I never even considered a university career. The situation in industry was hardly any better. As luck would have it, the small semiconductor research group at the Central Telecommunicat,ions Laboratory (FTZ) of the German postal service was looking for a “house theorist” who knew semiconductor theory, and I got the job. My duties were simple. I had to be available for whatever theoretical questions anybody had, and also take an active role by poking my nose into the work of my experimentalist, and technologist colleagues, to look on my own for topics to which I could contribute - provided I would never touch any equipment,. Every week or t>wo,I had to give a talk of 1 t o 2 hours to the group, on any subject of my choosing of which I thought that, the group should be taught about, it. Other than that, I
20 Selected Works of Professor Herbert Kroemer
was left completely free to pick whatever problems I felt were worth tackling. So I had become a “professor” of sorts after all, teaching a small but highly motivated ‘(class.” From day-1 I was forced to learn to communicate, not, with ot,her theorists, but with experimentalists and technologists. It was a fascinating challenge, with a range of topics far beyond what I myself had learned in Gottingen, very often going beyond physics, into metallurgy, chemistry, and electrical engineering. Of course I ceased t o be a “real” theoretical physicist) - if I ever was one. Call me an Applied Theorist if you want. However, the awareness of doing something truly useful helped overcome the uneasy feelings over ending a theoristJ career as soon as it, had begun. By hindsight, maybe it, wasn’t such a bad career move a f k r all! As my research topic at the FTZ, I picked the problem of the severe frequency limitations of the new transistors - and what one might be able to do about, them. It was this problem that led directly to heterostructure ideas. In a 1954 publication of mine there are a couple of paragraphs outlining in a rudimentary form the first ideas for what was later to be called the heterostructure bipolar transistor, or HBT. I proposed botJh a transistor with a graded gap throughout the base, and the simpler form of just a wide-gap emitter. The rest is history. This history is described in some detail in my Nobel Lecture, so I will give here only the highlights. Some time afterjoining RCA Laboratories in Princeton, N J , in 1954, I returned t o heterojunctions. I actually tried - unsuccessfully - t o build some HBTs with a Ge/Si alloy emitter on a Ge base. But my principal contributions t o the field were two theoretical papers. One of these, in the RCA Review, is essentially unknown to this day, but it clearly spelled out the concept of quasielectric fields, which I considered the fundamental design principle for all heterostructures. The final step came in 1963, while I worked at Varian Associates in Palo Alto, CA. A colleague - Dr. Sol Miller - gave a research colloquium on the new semiconductor diode laser. He reported that experts had concluded that it was fiindamentally impossible t o achieve a steady-state population inversion at room temperature, because the injected carriers would diffuse out at the opposite side of the junction too rapidly. I immediately protested: “But that’s a pile of ... ; all you have t o do is give the outer regions a wider energy gap.” I wrote up the idea and submitted the paper t o Applied Physics Letters, where it was rejected. I was talked into not fighting the rejection, but t o submit it t o the Proceedings of the IEEE, where it was published, but, ignored. I also wrote a patent,, which is probably a better paper than the one in Proc. IEEE. Then came the final irony: I was refused resources to work on the new kind of laser, on the grounds that there could not possibly be any applications for it. By a coincidence, the Gunn effect had just been discovered, and having a long-standing interest in hot-electron negative-resistance effects, I worked on the Gunn effect for the next ten years, and did not participate in the final technological realization of the laser. I left Varian in 1966, and in 1968 joined the University of Colorado. There I eventually returned t o heterostructures, and in the early-70s tackled the theory
Biography of Herbert Kroemer 21
of band offsets together with my student Bill Frensley - now at UT Dallas - who worked out, the first, ab-initio theory of the band offsets. Shortly afterwards - now at UCSB - I developed a powerful method to determine band offsets experimentally, by capacitance-voltage profiling through the hetero-interface. In the late-70s, I returned to the device that had started it all, the HBT. The technology developments that, had made possible the DH laser offered great, promise also for the HBT, and I became a strong advocate of developing the full potential of that device. In addition to heterostructures, 1 have worked on numerous other semiconductor topics, be it, in physics, materials, devices, or technology. Second only to heterostructures has been a continuing interest in hot-electron negative-resistance effects, dating back to my Ph.D. dissertation. I already mentioned the work on the Gunn effect, but there was more. During my RCA years, I had come up with a crazy scheme to obtain a negative resistance perpendicular to a strong bias field, by drawing on the fact that, some of the heavy holes in Ge have negative transverse effective masses - that is, perpendicular to their velocity. Experimentally, it was another failure, but, conceptually, I found it extraordinarily stimulating. So did others, and it earned me a great deal of early notoriety. Today, I am back to one of the sins of my yout,h: to the superlattice Bloch oscillator, an exciting combination of heterostructures and hot electron physics. AtJthe opposite end from hot electrons has been recent work on superconducting weak links in which a degenerately modulation-doped InAs/AlSb quantum well acts as a ballistic coupling medium between superconducting Nb electrodes. They exhibit some utterly delightful large discrepancies between experiment and accepted theory. There are numerous additional topics scattered throughout my career. I have basically been an opportunist - and not at all ashamed of it.
22 Selected Works of Professor Herbert Kroemer
QUASI-ELECTRIC FIELDS AND BAND OFFSETS: TEACHING ELECTRONS NEW TRICKS Nobel Lecture, December 8, 2000 bY HERBERT KROEMER ECE Department, University of California, Santa Barbara, C4 93106, USA.
I. INTRODUCTION
Heterostructures, as I use the word here, may be defined as heterogeneous semiconductor structures built from two or more different semiconductors, in such a way that the transition region or interface between the different materials plays an essential role in any device action. Often, i t may be said that the intmface is the &vice. The participating semiconductors all involve elements from the central portion of the periodic table of the elements (Table I ) , In the center is silicon, the backbone of modern electronics. Below Si is germanium. Although Ge is rarely used by itself, Ge-Si alloys with a composition-dependent position play an increasingly important role in today’s heterostructure technology. In fact, historically this was the first heterostructure device system proposed, although it was also the system that took longest to bring to practical maturity, largely because of the 4 % mismatch between the lattice constants of Si and Ge. Table I. Central portion of the periodic table of the elements, showing the element from columns I1 through VI actively used in current heterostructure technology. 11
111
N
V
VI
S
A1
Si
P
Zn
Ga
CC
AS
Se
Cd
I I1
Sb
T h 6 h school student. I certainly did not have any crackpot ideas. What would be an example of a crackpot idea? High school students often have crackpot ideas Such as building a time machine? Yes, or things that violate known laws - either because they don't know the laws or they feel they can violate them. I wasn't that type. You stayed at Jena for one year? Yes. Did your understanding, perspective or expectations of physics change during that year? That year had a great deal of influence on me, yes, because I was suddenly confronted with teachers who were really at the top level of their professioncertainly in math and physics. I don't remember any chemistry at Jena though I do remember some chemistry at Gottingen. I found one of the mathematicians at Jena very inspiring. His name was Brodel. In what way was he inspiring? He was an absolutely fabulous lecturer. I must admit that I didn't understand everything. That's the first time you weren't bored. It was the first time I wasn't bored but challenged. One of the reasons I was challenged was that in the first and second semesters I took courses intended for third and fourth semesters. I simply didn't bother with the first -semester courses. You had that option? They didn't force you to take the first as prerequisites? No, we could take anything we wanted. In physics, one of the professors was a gentleman by the name of Friedrich Hund. He was a spectacular lecturer and he had a great influence on my becoming interested in the deep fundamental principals of physics. Why was this? He is pretty close to the top of my list of people who should have gotten the Nobel Prize but never did. What was his area of expertise? He was one of the leaders -though not one of the founders - of quantum mechanics.There is something called "Hund's rule" which plays an important role in atomic physics even today. He was a wonderful teacher in whatever he touched, including quantum mechanics and thermodynamics. Itook a thermodynamicscourse with him. And he was a wonderful person. You took this course with him your first year? That was during that one year when I was at Jena. Do you recall your curriculum at that time? What did you take? I don't remember. You took thermodynamics and quantum mechanics?
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I didn't take quantum mechanics in the first semester. That came later. I really didn't have the background for that. In physics I probably took a classical mechanics course the first semester. That wasn't terribly inspiring. And it was probably in the second semester that I took the thermodynamics course from Hund. In the German system did they have what would be called auxiliary courses here in the United States, such as humanities? Did they make you take any courses besides those that related directly to your major? We could take anything we wanted. Anything you wanted? Yes. To get a degree one had to show certain pieces of paper. I was very much interested in taking courses outside of physics - particularly philosophy. You did? Interesting. I took a heavy load of philosophy. That's how I got into that trouble with that communist functionary in that class. Oh really? I took a heavy load of philosophy. I don't remember what the different topics were, but more than one course. I remember two of the instructors. One taught metaphysics. He was the one we applauded. Oh, that was the one you got in trouble for applauding. Yes, and lots of other things. Another instructor was a philosopher named Max Bense. who taught formal logic. He was fascinating. I have never known anybody who could construct sentences so long that were grammatically correct to the end. That is also a particular peculiarity of German, isn't it? Yes. How long did you have to wait for the verb? No, no. This is really not true that the verbs are always at the end. That really is bad German. It's allowed, but not a good practice. That is not what I meant. Did you mean clauses inside clauses and so on? Yes, yes. And the funny thing was that he said it in a way that it was understandable. I see. I found him interesting as a person more than I found the course interesting. Let me go back for a second. You mention rather brilliant people on the staff and at the University of Jena and you only spent a year there. What do you think the effect of Soviet presence was on that environment? It didn't do anything to the scientific environment, certainly not in those days, and I do not think it did much in subsequent years. But actually I wasn't there of course. It did nothing whatsoever to the scientific environment. The influence was in the political environment and the everyday environment. I had fallen in with a group of students who were all very liberal and I had the suspicion I was being noticed. One of the depressing things was that over that year every week one or two people would disappear. Really? One never knew whether they had lefl by their own free will or ended up in the gulag. I see. The gulag in those days meant the uranium mines at the Czech border. This must have been an environment of great uncertainty and fear. Yes, yes. We could not trust anyone we did not know personally. You said your time at Jena was important in your formation and that it had changed you somewhat. It really exposed me to physics. Did it also expose you to other good students? Yes, absolutely. They played an important role. Were you considered a bright student at this level yet? Probably, yes. Nothing indicated this officially, but I think I was one of the better students. There is one interesting difference in that education system compared to what we are doing here at UCSB. For example in the calculus course. Homework is an integral part of the course in the United States, but the way this was done there was that there were problem and homework sessions. They were different courses, and sometimes they didn't have too much in common with one another. I knew calculus pretty well already. We had calculus in high school and I had studied it on my own - but not in the rigorous sense in which it gets done at the university where one worries about all sorts of things that could go wrong. The way I learned it one did not worry about things could go wrong. This makes one better qualified as a physicist. Yes, I was going to say that. That instructor was pretty boring, so I went only to the problem course. I needed that certificate that I had attended that course two semesters in a row. And that one was fascinating. There I found a real challenge and I got one of the top grades in the class. They congratulated me. I remember it was a lady who was teaching that one. When she was handing out the certificates at the end she said, "I hope to see you again" in the sense that I was one of the ones they wanted to see. I enjoyed it. I'm curious. With two courses, one solving problems and one for just theory, how were you tested in both? The test would seem to be the problem solving. The test is the problem solving, yes. I never went through the mainstream course. First of all I discovered very quickly that I already knew everything that was needed to solve the problems and it required more imagination as to how they could be tackled. That was the good part. Also in the physics courses the problems session typically was separate. In that other course with a mathematicianwhom I admired there was also much homework.
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At this stage, after one year's exposure, did you start to see a sense of what kind of physics you wanted to do? Not really. It was a wide-open field, but it was very clear that I enjoyed physics. I want to pursue this thing about you winding up in West Berlin. You said four of you had a summer job at Siemens. Yes. One of us had arranged that summer job at Siemens. At this point there was not much impediment to travel from East Berlin to West Berlin and work? No, it was still completely open although this was during the Berlin blockade. The blockade referred to truck trafflc, rail traffic and bringing supplies into Berlin, but there were no limitations on people crossing into Berlin or within Berlin and crossing between East Berlin and West Berlin. Then you go on to say that at that point you decided you were not going back because of this uncertainty and fear you were experiencing in this environment. Berlin during the Berlin blockade was an exhilarating experience. In what way? First of all the West Berlin government was about as firmly anti-communist as could be, even though the mayor was a former communist. He had turned anti-communist. What was his name? Ernst Reuter. He was a fascinating man, and I remember going to one of his big speeches. One of the interesting experiences I had was one of the airports which sewed the airlift - the airlift was functioning pretty well by late summer - was the Tempelhof Airport, which is basically the airport downtown. There is a railroad track along the edge of the airport and that is somewhat elevated, and in the evenings we often took the train to Tempelhof Station just to watch the aircraft take off. It was a fascinating experience. What was so great about it? It was staggering how well it was organized. The Soviets could have stopped this whole thing with one fighter plane, but they didn't dare. There were two runways - one only for takeoffs and one only for landing - and they were bringing in planes roughly at the rate of one every 75 seconds. wow. You could see them along the horizon like pearls on a string. The pilots didn't really know to which gate they had to go, so next to the runway were a number of jeeps and as soon as the plane had slowed down so that a jeep could keep up with it the jeep pulled in front of the plane with a sign, "Follow me." Really? That jeep driver knew which gate had just been opened. Oh, I see. That made you believe in Germany and America having something in common. The efficiency? No. You see, in '47 and '48 it was not clear whether Germany had any future, but it was very clear that if there was a future for Germany it was in alliance with the United States. Amazingly, even though Berlin had been badly bombed out by the Americans and the British there was basically no resentment by the people. That surprises me. Was that because the communists were there? Yes, well, the contrast was stark. Okay. The four of you were watching these planes coming in and leaving and then the thought came to you that you were not going back? I decided I was not going back. Were you ever personally frightened? I know the man that stood at the door said, "We're going to watch you." Was it a serious consideration for you that, "Maybe 1'11 get in trouble if I stay in East Germany"? Yes, but nothing specific. Yes. It was more than just vigorously disliking the environment. I was also worried that I might be forced to do something. The physics education was good in itself. Yes. It was other considerations. Gottingen was the top university. But at that time you didn't know about Gottingen? I knew about Gottingen. I mean as an option for you. It wasn't a real option yet when you made the decision to leave? I had written to several universities in West Germany and applied to each. Gottingen was one of them. Gottingen had actually turned me down, but I never got that mail. Fortunate for you. I had a recommendation from one of my Jena professors. I had gone back to Weimar to pick up my baggage before leaving by way of Jena. Professor Buchwald suggested, "Why don't you see Professor Konig and see what he can do for you?" Konig was an old friend of his. I see. I was staying Kassel. which is where relatives of mine were living. It is just about a half hour from Gottingen by train. Was it a difficult decision for you to head out and leave your family behind? It must have been. Or was it something that you didn't have to anguish over much because you were too worried about staying? It wasn't really difficult. but probably one of the reasons it wasn't difficult was because I didn't appreciate how difficult it might turn out to be. What did you later find? Well, my parents could no longer support me. The currency differentialwas such that it was totally impossible. I had to find a job. It was an interesting exDerience.
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After the walls went up and other things that happened you must have been cut off from your family. I went back for a visit a few times. Weren't you worried about being caught? Oh, I was always absolutely terrified. Was your father supportive of your leaving? He didn't try to talk me out of it. He probably realized that this was perhaps the best thing for me. He didn't actively encourage me. However neither he nor my mother made any attempt to talk me out of it. They said, "All right. If that is what you want to do, then go and do it." You also write that you found Gottingen to be a wonderfully stimulating place. It was absolutely wonderful. Was it the same kind of stimulation you found in Berlin? What was it intellectualstimulation that you found in Gottingen? Yes, it was intellectuallystimulating. Gottingen was always one of the top universities in physics in Germany, and in fact in science in general. During the twenties and thirties Gottingen. Berlin and Munchen were the leading universities in physics. Gottingen had not been bombed out during the war, and as a result many academic people who were refugees from the East congregated there. There were a few what is now called Max Planck Institutesthough they didn't have that name at the time. It was an absolutely fascinating collection, absolutely fabulous. Tell me about your process of your getting into Gottingen. You said you were initially rejected. I showed up in the office of Professor Konig and he said, "Admissions are closed and there is nothing I can do," but somehow he decided to take me on a tour anyway. Maybe he just wanted to be nice or maybe he had some afterthoughts. I don't know. I showed up in the office of Professor Richard Becker and had a nice long conversation with him and he asked me many questions. His assistant, Dr. Gunther Lelbfried, was also there. They spent a long time with me and then passed me on to Professor Wolfgang Paul [Nobel 19891and Professor Robert Pohl. Gradually it dawned on me that these were not just social conversation. I was in an examination. Did you start to worry at that point? No. I remember one of the exam questions given to me by Professor Paul. 1'11 neverforget it. He said, "Mr. Kroemer, you know that a mirror interchanges left and right." I said, '"Yes." He asked me, "Why then doesn't it interchange top and bottom?" What was your answer to that? I gave him the answer. The answer is it doesn't invert left and right. That's all he wanted to know. However it must have been very obvious that I had to think about this first. At the end of all of this I was led back to Becker's office and they said that admissions were closed but they had received notification from two people who had been admitted that they were not coming. Therefore they had two openings and that within the next day or two they would decide who would get those two openings. They explained that if I was chosen Iwould receive notice. That was on a Thursday Ithink. The next Monday or Tuesday I received a postcard notifying me that I was admitted. How did you support yourself at that time? That was difficult. I found a job in a local aluminum cooking ware factory Lots of students where employed there during the night shift. What did the students do? We operated the equipment and did whatever jobs had to be done. It paid well enough that if one was frugal one could survive on it. That must have been tough working night shift and studying days. Yes. it was tough. One summer I worked in a coal mine. I wanted to ask you about that. What were you doing one kilometer down in a coal mine? It wasn't a neutrino experiment, was it? It was not a neutrino experiment. It was a very interesting experience. I don't remember the proper English terminology for what I was doing. Hard coal was being taken out, and of course on the surface of all of this is the dense population of the cities in the Ruhr Valley. In order to keep the surface from collapsing they tried to refill this after the coal had been taken out. It was being refilled with sand typically, and sorts of other debris. I worked with that crew. And it was strenuous work but it paid well. For he first time in my life, I was embedded in an environment as a lone student amongst coal miners. I suddenly realized that these people didn't have as much. How did they treat you? Very, very nicely. They always assured me, "At least you know that you will get out of this one day. We are going to be stuck here the rest of our lives." I suddenly understood why people like this were voting communist. Not that I agreed with them. Right. I understood their demoralizationand their expectations and their feeling that the political system would not take care of them. That changed later on, but this must have been '48 or '49. That was a tough time economically.All of Europe was in ruins in a sense. Yes. Now that was during the Marshall Plan year during which time Germany was recovering rather quickly. The coal industry was one of the driving engines of the recovery. It was a very interesting experience. Referring back to your autobiographicalsketch, you highlightedvely briefly the deep influence that Dr. Fritz Sauter had on you. He was your Ph.D. supervisor. wasn't he? Both my diploma thesis -which is sort of a master's degree -and Ph.D. supervisor, yes. Would you explain more about his influence on you? Ours was not a close personal or warm relationship. It was a purely professionalrelationship.
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You wrote, "Under influences such as these I never developed into a hardcore Theorist with a capital T but became basically a conceptualist." Yes. What does that mean? Let me go back a few steps on that one. One course that was very important for me throughout my years in Gottingen was the seminar in theoretical physics. This was not a regular course but a sort of special topics thing where the instructor handed out material and assigned papers. The students were required to read the papers and then report on them. I found this a very stimulating environment. I had participated in these kinds of courses right from the beginning of my Gottingen days. Sauter led one of those courses. I got some assignments, and one of those assignments led to a master's dissertation. What was that assignment? I was already going toward solid-state physics. That assignment was studying certain things that happened in periodic potentials when some of the parameters are changed. An interesting aspect of Sauter's style was that he didn't call on students to report once or twice a week or on any regular schedule. He basically was available when he was needed, but he left the students alone. He was basically watching and forming his own opinions as he watched. I remember one time coming to him with an idea I had, a physical concept. He listened and then said with a tinge of sarcasm, "Well, Mr. Kroemer, that's all very nice, but you ought to be able to formulate this mathematically." At another time I would report to him how I would formulate something mathematically, Obviously mathematics was Important Then with a slightly more sarcastic tone he responded, "Mr. Kroemer, this is just a piece of math. What does it mean physically?" Once one goes through this loop a few times one gets the message. One gets the message that one has to be able to move at ease from one to the other in order to live up to Sauter's standards. That was a deep and formative experience for me. I have later on encountered the same thing with Bill [william] Shockley. whom I knew quite well. Shockley had that same style. moving back and forth. There IS something else that happened too. We had already agreed on the topic for my Ph.D. dissertation while I was still working on my diploma thesis. One day Sauter came into my office and told me to stop working on the diploma thesis and simply write up whatever I already had and submit it. I protested, but he said, "Never mind. Let's move on to the real thing." He was also wonderful in the sense that he didn't believe that degrees should be awarded on the basis having served time. Yes. I like that statement. First of all he didn't have any money to support his students. Sauter's idea was that he was watching people and to him a degree was to certify that this person could do creative and independent work on a certain level and that as soon as this level had been reached -get out. That was very good for me, because I had to earn a living. I got my Ph.D. a few weeks before my 24th birthday. That's remarkable. Five years of total experience between entering and leaving. Was that unusual? That was unusual even for Gottingen, yes. I was one of the youngest Ph.D.s in physics after the war. And that would not have happened under any other professor. Right. The way I ended up with Sauter was different. I had originally attached myself to a person who at that time didn't even have the professorial rank. He was a lecturer and instructor: "Privatdozent" Dr. Hellwege. I also had a very close personal relationship with Hellwege and had signed up for a diploma thesis with him. However he had an awfully long waiting list. Then Sauter offered me the opportunity to get my diploma under him. I talked to Hellwege and he said to me, "Kroemer, take it. You will be finished with him before you can start with me." This is how I ended up a theorist. Sauter was a fabulous mathematician, but to him it was a tool. To him ultimately physics mattered. You made the distinction that you were a theorist but not a hardcore theorist. I wasn't. I was a conceptualist. What does that mean? There are theorists that know only theory and are heavily engaged in mathematical formulas, whereas to me the mathematical formulas were never more than a tool Mathematics always represented something to express physical ideas and the physical ideas were always related to experimental facts even though I was a theorist. And I never was a good experimentalist. You were never a good experimentalist? No. I think I was good at picking good projects. What does it take to be a good experimentalist? I don't know. Not having been one I could not say. What couldn't you do? You must have come to the conclusion you're not good at it or didn't like it. It is not a matter of not liking it. Some people have the touch. They invent their own equipment and build their own equipment. I was better at thinking about what equipment one should build than at actually building it. Okay. A conceptualist. I was a conceptualist. I see. You made the interesting remark that your role model was more Niels Bohr than any other great physicist. That's right. Yes. What was it about Niels Bohr that attracted you to him as a role model? Conceptual depth combined with very simple mathematics. He was an ideas man.
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I don't want to be too simplistic about it, but what about Einstein who did a lot of mathematics and had conceptual ideas too? Actually Einstein is really a conceptualist. The mathematics of course came with the general theory of relativity. He got his start from Minkowski on that one. In his later years his work was very, very heavily mathematical. However that didn't really start until 1920s or thereabouts. He was really a conceptualist. Just for the fun of it, I have been rereading some of Einstein's early papers on statistical thermodynamics. The concept of wave particle duality shows up in Einstein'swriting before DeBrogiie. That's amazing. Not in the same formulas. Do you see anything else in Einstein's early papers that strike you after all these years? Are there any surprises? Yes. it surprising in the sense of just how brilliant Einstein was, and what a fabulous instinct he had. He anticipated ideas that were not accepted until much later on and helped others get on their way. For example de6roglie's thesis. I don't remember who his thesis advisor was in France. I can't remember either. Thesis advisors played a different role in those days. One turned in one's thesis and the thesis advisor was the person who was supposed to judge it. In a way Sauter was like that with me. He simply watched and when he saw a final draft he criticized it. Anyway, deBroglie's thesis advisor didn't really know what to do with deBroglie's thesis so he turned it over to Einstein. The remark that Einstein supposedly made in regard to deBroglie's thesis was, "He lifis a great veil from the secrets of physics." I am certain that Einstein had anticipated something like this. The history of physics is fascinating to me. Yes, it's interesting. And yet Einstein is always attributed to saying that God doesn't play dice. His resistance to quantum mechanics. His resistance to quantum mechanics was first of all that he definitely did not like the probabilistic interpretation. Yes. Probably what disturbed him more than the probabilistic interpretation was what we today call the non-locality of the theory. It contained an aspect of action at a distance. That was probably more disturbing to him. I've done a little bit of reading on what exactly Einstein opposed. There's the famous Einstein-Podolsky-Rosenargument. It was entirely consistent with Einstein's thinking in the early days. Having been a participant in writing a book on thermodynamics, I have seen that what is today attributed to Boltzmann was really first clarified by Einstein. Really? Einstein took Boltzmann's ideas and put some rigor into those concepts. Very interesting. That is somethina I discovered onlv recentlv. I became interested in Einstein basically while t&ng 10 unoerstand more abobt the history the Nobel Prize Having receivea that prize I decioeo to find out more aboLt what makes tnat system tick have you founo o(r1what makes i t tck? I founo oLt a lot becaJse lVe been reading on that Of coLrse Einstein's hobel Prize was an extraordinarily controvers a, In ng Was 117 Yes n e had been nominated a nLmber of tomes for tne theory of re at vity and the people who controlled the pnysics Nobel Prize at tne Royal Acaaemy were absolutely opposed to this one One of the key members of the phys.cs committee is on record as saying "Einstein will never get the Nobel Prize Planck had trouble too Anyway. this is why Einsrein endeo bp getting the NoDel Prize for the photoelectrc effect rather than the theory of re,atlvity Okay The political shenanigans of how this was pulled off nave been descnbed rather beaLt,fully in some books I became interesteo in exactly what Einste n's role was oLtsioe of quantLm mechanics and relativity becaLse of his role in thermodynamics Einstein ha0 a role in thermOOynamiCS? AbsoIute,y I see ThoLgh I studieo Einstein. I was nor aware of that From this kind of exploration yoL've been doing. do YOL feel that it IS important for physics majors to take a coLrse in the history of physics to Lnderstand the development of their profession? I oon't know how imponant it is i certainly do not believe that physics shod0 be taLght in the histor.cal order at all The nistoric aevelopment of tne felo of physcs contains a staggering number of blind alleys m ' t that important for people to bnderstand? It is not imponant for Lnderstanoing physcs However it IS imponant in a CultLrai sense I personally am fasc.nateo by the hlslory of physics - by dll the blind alleys and by all the mistakes that were maoe An0 i t s a story in nunan cLlture However I am opposed to teaching physics. part.cularly qdannm mechanlcs. In a historcal context But as a c o m e in history? Yes Would you recommend that physicists also take a course In the history of physics?
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Iwouldn't want it to be a required course, but Iwould highly encourage taking such a course taught by someone who knows what he or she is talking about. Friedrich Hund, who I mentioned earlier, wrote a beautiful book on the history of quantum mechanics. I do not know whether it is available in English translation. I read that one twice, which is something I don't do very often. He actually argued that the natural road to quantum mechanics was through thermodynamics rather than through spectroscopy. Through thermodynamics? Yes, and I never accepted this thesis of Hunds - until I read the Einstein papers. Really? That is the conventional wisdom that the road to quantum mechanics was through spectroscopy. Yes. Max Planck's blackbody radiation was an exercise in thermodynamics. I see. The idea was that electromagnetic energy might be quantized. which Planck himself did not accept initially. That of course blocked his Nobel Prize for many years. It did? It was obviously ridiculous. All one had to do was look at the diffraction experiment to realize it was a continuous wave. This is the resolution of this one. Einstein was simply the first one who decided to simply ignore the discrepancy. You just mentioned earlier about Sauter's views about degrees - not serving time but proving a certain capability to execute independent work. Do you take this approach with your students in the system that you have here in the United States? To the extent I can, yes. I am of course under some constraints. There are certain rigid requirements. I encourage my students to spend at least part of their time working on projects other than their own research projects in order to get broader experience. The overwhelming majority of the Ph.D. dissertations that I have supervised were experimental work. Really? And that doesn't go quite as fast as a theoretical dissertation. That's an interesting contradiction for someone who said he wasn't going to be a good experimentalist. I think I was pretty good at identifying projects that are worthwhile, and in a semi-facetiousway I would like to add that maybe having been a theorist and thereby not knowing how impossible it was to do those things being proposed has helped in actually getting them done. You see, if I had grown up as an experimentalist I would have had a far greater appreciation of the difficulties of doing the things that I wanted done than I have had as a theorist. This has probably helped me. I do not recommend this as a universal procedure. I remember for example how I got into molecular beam epitaxy. How was that? There was a technoloav that I felt was makino thinas Dossible that had previously not been p&ible. Therefore I proboseitd put gallium phosphide on silicon. And of course if I had been an experimentalist I would never have proposed to put gallium phosphide on silicon because it was too obvious that this would not work and what the difficulties were. Well. we did it. I see your point. Sometimes a little ignorance is useful Yes, but you shouldn't count on it. Luck is good too. Along these lines about an educational approach to what becoming a physicist means, the chief editor of the IEEE Spectrum wrote about you in the 2002 issue of that publication. In it he says, '"To this day his [Kroemer's] view of education is that accumulating methodology matters more than accumulating subject matter knowledge." Absolutely. Would you please explain? In my own mind a methodology is a form of knowledge. By accumulating I mean accumulating data facts and details. I think the question is of how one goes about solving a problem. How do you estimate what problems you have to solve on the way? How do you estimate the chance of success? This to me is far more important. Can that be learned or is that something one gains from experience? Is that something that can be formally taught or is it something that can only be gained by experience through trial and error? I think it can be taught to some extent. What procedures do you use to teach this to your students? By always insisting that whatever they are doing is not simply done following the recipes, but that they understand the rationale behind it. In this context I have a story to tell. In January of 2001 I was invited as a keynote speaker to a workshop held by the German Ministry of Research and Education at Stanford University to an audience of something like 150 to 200 German Post Docs. Were these Post Docs from all fields or just physics? From all fields, and under the jurisdiction of Madame Edelgard Buhlmann. who was then and is still now the German Minister of Research and Education. She was very, very much interested in university reform. At this workshop somehow it got mentioned that I had received my Ph.D. before my 24th birthday. One of the Post Docs in the audience burst out, '"Butyou didn't know anything yet at that time." Which was referring to the deplorable tendency of having people study a lot of material rather than concentrate. Just for the sake of it you have to know it all. Yes. I was tempted to answer, "Well, it didn't stop me from getting the Nobel Prize," but I didn't do that. It would not have been nice. I simply said, '"Listen. I had learned how to tackle a problem even If I had no previous background in the details. And I feel that was important." That's very interesting. That explains the distinction to me.
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Knowledge of detailed subject matter becomes obsolete. Why would you want to cram your brain with detailed subject matter long before you actually need it? Learn how to find it. I see. Richard P. Feynman once made a similar comment. He did. Somewhere in his writing there is a comment that he didn't see much point in reading up on what all the others had done because they had obviously not succeeded. I sympathize. I agree with his point of view. Now if you are interested in the history of the field then of course that becomes a different thing. I do not view the history of science as a tragedy: I view it as a comedy. But you know tragedy and comedy are very close together. Yes, I know. Maybe personal tragedy with the blind alleys and the narrow-mindedness with which representatives of the established power structure often suppress things that they don't like. Do you remember the famous quote from Max Planck, '"Theoriessucceed because their opponents eventually die off'? The trouble is, it applies to him too. Yes, I remember this from his autobiography. He was advised against studying physics because there were no problems left. Yes. Philipp von Jollv was the name of his Dhvsics Drofessor at Munchen who aovised him that w,th the oiscovery of the principal of energy there were no more problems left All the rest was just worming OLI the details Fonmately Max Planck went on to pursue physics He was basically a very conservative man He slruggleo for years trying to overcome and Lndo the revolLt on he hao started He did? On yes For years he trieo to invent this back into a classcal framework - m total contrast to €insteon The two respected each other trernenaoLsly Einste n seemeo to enjoy overthrowing sLch concepts I see In 52 YOL gradLated at 24 you got y o u Ph D and you wrote that there were not many opportunit,es for advancement in acaoemia at this point even for a bright theoret clan like yodrself Yes Zilch Zilch Nothong F rst of all there were no new Lniversities no new departments being formed and there was a long w a m g list of people with first rate credentials an0 more seniority waiting for any openings It was sort of a dream but I &led it OLl
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B L it~ was something YOL WOLIO have loveo to do ifyou had the oppondnity? Yes I WoLld have loveo to do 11 I simply consioereo the opportLnity to oe zero - which was a correct assessment for the oay It Iurneo oLt the other option ha0 ramifcations for YOL You said that at the Central Telecommunications Laboratory you were a nouse theonst That s a verbatim translation from the German That's a common concept What did this position entail an0 how mLch latituoe were YOJ given to be hoJSe theorist7 The posit on entaileo to be available to try to answer whatever theoretical questions came up That was the minimLm bLt more than that I was really expected to take dn active role To seek the theoretical issLes to what they're doing To seen ano to try to take an actwe role in making suggest ons I was encoLraged to actively poke my nose into the experimentaltsls business now dio they react to your presence? I was strictly forbidden lo toJch any eqLipment so was not a compet tor t was a good relationship They value0 your inpLt rather than saying '"Whatdo we need thls theoretica s t ~ ffor7 f ' Another one of the things that I was expecteo to 00 - every week or every other week - was to give a IectJre to anybooy who wanted to come ano I sten on any subject of my choosing Naturally I picked sublects tnat I felt were relevant to the work tnat was going on Was th s well received? Oh yes That very ohen involved me having to learn new things I had never in my unwersity career seen a metallurgic phase oiagram I discovereo very qLickly when I tried to unoerstand on what principles these recipes were based that we were Lsing make transistors that I had to learn a little bit of metallLrgic phase oiagrams Teaching others is a much better way to learn something so I thoroLghly enjoyed this work an0 I Inink I was goo0 at it YOL wrote that this job was an important landmark in your development as a physicist YOL commenteo "I cease0 to be a real theoretical physic st 11I ever was one I took that in a positive sense in that you f o w d youself having to brioge between theory an0 practice a lot Yes First of all I was in an envjronmenl where I was bastcally not interacting with other theorists I was in an environment where I was interacttng with experimentams I was the theoretical advisor And of c o m e I was encoLraged l o follow LP theoretical oevelopments ,n the IiteratLre I was never qLalfieo as a 'real' theoret cai physicist If I ever was one Whatever that means I think when it comes to a Professional Theorist with a capital P and T I am not considereo a theorist An0 I do not cons oer this a negative assessment The important question is not 'Are you a theorist or are YOJ an experimental,sl~,'The imponant question is 'Are you oong something Inat is useful? Are yob contriouting7" Let me see if I can provoke YOL to say something controversial In general 11'svery easy Do you feel that in some areas of physics there tenos to be an overempnasis on theoretical formalism in pursuing theoretcal issues'? 'I
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I don't know whether it is characteristic of the area. It's probably characteristic of some individuals in all areas. Some areas of course lend themselves more readily to this than others, but I would not want to disparage any single area of physics in particular. And I shouldn't comment on areas that I don't understand anyway. But it certainly is clear that in all areas you find a broad range of people with different interests, from the pure empiricist experimentalisttechnologist who has not the foggiest idea of the underlying theoretical principals and not caring. Then there are peoDle at the other extreme who see only mathematical formalism. They like elegance. They like elegance. I like elegance too. But elegance for the sake of elegance as opposed to elegance for the sake of a physical principal. Yes. It is a broad spectrum. I was thinking more of the areas of the Grand Unified Theory I find this a fascinating human exercise. I can see why it appeals to ambitious young people who are doing theoretical analyses that this is the great problem to be solved. I understand this. The question is what do they do when they realize that there is a fierce competition? Thus far no one is making any progress. I wish they were a little broader. There are a lot of shipwrecks on that rock. My recommendationto somebody who really is interested in these deep profound principals is sure, do that, but do not restrict to yourself to just that. View this as a part embedded in something much broader. I see. Getting back again to the Central Telecommunications Laboratorv. in Germany its acronym is FTZ. What does that stand for in German? FernmeldetechnischesZentralamt. Fernmelde is telecommunications, technisches is technical, zentralamt means central office. Okay. I know you answered this before but I have to ask you this anyway. Did you have close interaction with these experimentalists and technologists? Yes. Do you think this sharpened your skills as a physicist in a way you would not have gotten if you had stayed in academia? Probably yes. I don't know whether it sharpened my skills as a physicist, but it certainly broadened the range of things I was thinking about. It was again methodology,and I was taking an active interest in how one could do this, how I could implement this I was taking an active interest in trying to understandfirst of all what we had done and then going on from there and saying, "Allright, now that I understand, how could I modify it to do better?" It was like a pendulum swinging back and forth. That has a great influence on me that continued in my subsequent jobs. Would you say that in a sense this experience brought out your versatile talents as an astute problem-solver -- what you call an opportunist? Was this the first seed of you acting like an opportunist? Yes. In a good sense. Yes. It always shocks people that I call myself an opportunist, because it's always a dirty word. But I deliberately use it - perhaps for the shock value because an opportunist is somebody who is looking for good opportunities to do something. The right problem. Yes. I want to get to that, because that's an important theme choosing the right problem. I want to ask you a broader issue here on the different levels of knowledge and methodology. In your career your research has bridged the realms of theoretical physics with a small "t". applied physics and whatever that means and electrical engineering? Yes, although I am not really an engineer. My degree in engineering is honorary. Your understanding of some of these issues has been an important part of your work. Looking back over the growth of science and technology in semiconductors,how would you characterize the body ofknowledge in each of these areas and how they interact at the interfaces between theoretical physics, applied physics and electrical engineering? And has that direction changed over the last fifty years? I don't quite know in which terms to answer that one. After all, you are in an engineering school now. I am in an engineering school and I feel very comfortable in an engineering school because I bring to bear my scientific background to solve problems and to contribute to engineering developments. However I am basically still a physicist. Throughout my entire career whenever I was working on something and then discovered, "Hey there's something else you have to learn in order to able to do this," I have always tried to acquire this knowledge. Therefore I have a background - though an extraordinarily sketchy background- i n electrical engineering I know those parts of electrical engineering that I need and I know those parts of theoretical physics that I need and those parts of mathematics that I need. I think the field as a whole has required and has benefited from the broad assortment of people in all of those particular disciplines from theoretical physics to metallurgy to you name it.
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Those laboratories where the important contributions were made typically had organizations with a broad range of people from different backgroundsto the point that an individual's background was often not known or even a concern. bcertainly learned that in the three years I spent at RCA Laboratories. Where the problem is the important thing. How the problem is tackled and one's background doesn't really matter. That's right. That's interesting. Is that something that you feel has implications as to how universities should train people in these fields?
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To some extent this is a matter of education at the university, but to a large extent it is also a matter of personality. I believe that an in-depth education in some specific discipline is important. Yes. In my case it was in theoretical solid-state physics. All the other things got added on later. I do not believe in giving people a superficial education in a lot of different things. An in-depth education in the specific area is important, but it also requires an attitude to be interested in what goes on in adjacent fields, trying to interact with people in other fields, trying to contribute to their experiments or projects and having them contribute to your projects. I guess the issue then is not the knowledge but the attitude to look to the other people. Yes. For example I think it is important that physicists not take the attitude that pure physics is something more elevated than applied physics. One sometimes finds that attitude. Then in engineering the opposite attitude can be found which looks down on anyone interested in theory or in something for which an application is not already known. Yes. You know how hostile I am to that idea. Yes. 1'11 get to that. That's interesting. I think universities can contribute to this in two ways. They can obviously contribute by providing the specific knowledge that is required. There is always hope that along with that specific knowledge there will be instilled a desire to do more than just a specialty. It is desirable that we combine these two aspects and see this embedded in a broader framework. Of course this will depend on the individual, the faculty and the university environment. Am I correct in judging from what I read that the embryo of your ideas on heterostructure bipolar transistors first came to you while you were in the Central Telecommunication Laboratory? That's right. And then you write '"andthe rest is history." Yes. How did the idea come to you? Was it a natural progression of your dissertation? It had nothing to do with my dissertation. Was it the environment you were in that prompted you to think about this? Yes. We were working on the very early transistors. They were so slow that they were basically useless for the applications on hand at the time. I realized that an earlier incarnation of transistors - the first so-called point contact transistor that didn't have junctions inside - talking about bipolar and not FETs -were significantly faster than the first junction transistors. And there were a variety of reasons for that. One of the thoughts that came to me was, ''Well, we do know that in the point contact transistor the collector is very leaky." In other words it draws a rather large current by itself without an injection of holes or electrons or whatever it is from the emitter. Of course this leaky collector film introduces an electric field in the body of semiconductor around the collector in such a way that carriers of the opposite polarity were drawn towards the collector. So that was my point of departure. I'd say, '"Howcould you build an electric field into a junction transistor?" That was your key idea? That was the key idea and not by doing s leaky collector. The first idea then was, "All right, we are putting a non-uniform doping into the base," and specifically I looked at an exponential doping profile. You can then show that this leads a built-in field that speeds up the carrier. And that required an understanding of band structure. This is where theoretical issues came into play. This is where my understanding of basic semiconductor physics told me that it should work. I see. Then at one stage the thought occurred to me that another way of putting in a field is to use a non-uniform energy gap. And this is the theory. Okay. Did this idea come immediately after the first idea? How did this idea emerge? I don't know what immediate means here. Did it take a year? Less than a year. It was part of the same work. Okay. The idea came then that a field could be built in by grading the energy gap. Did something prompt you to think of it? It was obvious. It was obvious. Why hadn't people thought of it earlier if it was obvious? It was not obvious to others. Well, let me say it was obvious because I had a goal. I wanted to put in a field, I needed a sloping band and I realized that I could create a sloping band. You see I always try to view those things from as fundamental a point of view as possible. The need for a band slope was the key idea. The field needed a slope in the band and I realized fairly quickly that a second way to introduce a slope in the band was to grade the energy gap. Okay, so that's the succession of ideas. Once you committed to a sloping electric field then that led to the next idea.
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Yes. There is a comment in that first German paper on that one and I estimate what kind of a potential drop could be obtained in the band. It was a bit optimistic. These things are always optimistic. I looked specifically at germanium-silicon,not realizing that there were very. very severe problems there. Anyway, my technological colleague, Mr. Hahnlein, was basically the physicist working on the device technology. He looked at this and said, "There is no way I can do it. The most I can do is perhaps put an emitter with a wider energy gap on the base region, but I cannot put a control field in the base." Of course that would mean a uniform gap in the base region -and that would mean that the field that Iwas trying to achieve would not exist. So that idea was out. But then on the way home, out of sheer curiosity, I wondered, "Well, what would be the consequences if that was done?" And I realized that this would have unique benefits of its own. The repulsive barrier at the emitter side would be increased for those carriers flowing from the base back into the emitter. That could now also be traded off with other things. This is how the wide gap emitter and the graded gap arose within days of each other. They are both in that first German paper published in 1954, so the idea probably arose in late '53 -though, in that paper it was unfortunately not accompanied by a band diagram. The idea that one has to be able to draw a band diagram came shortly after that. It seems like you had considerable freedom at this place. I could work on anything I pleased. And you found the work quite stimulating I imagine. Yes. And yet you wanted to move on. Well, I wanted to get involved closer to the action. I gather you first thought of the opportunity with William Shockley Shockley visited our place and I had a long and wonderful long discussion with him. I asked him about the chances of coming to Bell Labs at that time. He was reluctant in his response, because he was an official visitor. Official visitors are not stealing people. Oh yes, of course. I think his reluctance regarding such matters later decreased. He said, "You will have to take the first step." And then there was Ed Herold from RCA whom I had met at the Physical Society Meeting in Innsbruck. He didn't even know about the existence of our laboratory but I got to have a long discussion with him. He had presented an invited paper which pretty much confirmed everything I had claimed about how what was going on with the metallurgy that some people didn't believe. It turned out he had a day open on his agenda and so he came also to Darmstadt to the FTZ [Central TelecommunicationsLaboratory] and I had a long chat with him. When I asked him about the chances he was not under the constraints that Shockley had. A good question is why I ultimately went to RCA rather than Bell Labs. Yes. That's a very, very good question. In fact Bell Labs was offering more money when it finally came to the details. And what was it? I don't know Jim Early said to me, "Herb, you may have felt that at Bell Labs you would always be in Shockley's shadow whereas at RCA you would be your own man." That may have played role in my decision. I do not know. That is speculation. This is sort of tabletop psychiatry. Well, let's go forward. What were your impressions of the people in research when you got to RCA Labs? Oh, it absolutely fabulous. Can you recreate what you saw and felt when you first got there? It was simply a different world. There were lots of people, many of them very good people, working on all sorts of aspects. It was an environment where free discussion across disciplines was very, very much encouraged. A theorist who wanted to do an experiment was not talked out of it because people saw no need for it. I said, "All right. Go ahead." It was a wonderful lab and I was surrounded with wonderful people. The ones who influenced me most were perhaps not the ones who were best known. Who were they? One particular guy who influenced me tremendously was an office mate named Lou Pensak. He had been heavily involved in the technology of television tubes. He was a constant discussion partner and also introduced me to the idea that if you want to build something the right tools are needed -and the tools should be built first. He had a great influence on me. It was a fascinating laboratory. Ed Herold was a wonderful boss. It was a great experience. Now this discussion with Ed Herold in Darmstadt was interesting one. You see I understood the metallurgy of those transistors in those early days. They were pnp transistors that had indium alloy to hvo sides of a germanium wafer. I was curious about npn transistors. I tried to think about how might one do an npn? I couldn't get anyone interested in actually doing it, but I sort of figured out what I would do if I were asked to build an npn. So I asked Herold whether they had also made npn transistors. He said yes. I asked, "What did you as the alloy metal?" He was a little bit reluctant but answered, "Lead." To me it was clear that it was either lead or tin, and for reasons that I do not remember I thought lead was the likely candidate. I said,."But lead is not a donor, so you must have added something else." Long pause, more reluctance. "Antimony," which I thought all along was they had. Then I asked, "Well, how much antimony and at what temperature did you alloy it?" He clammed up. So I told him "You use 9 percent antimony and alloy it at 60W." And his jaw dropped. It was sufficiently close to what they were actually doing. It was a living exercise in the old rule "Never mind how something is done. Knowing that it has been done is the biggest secret of all."
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Is that what convinced him to hire you? I don't know whether that convinced him, but certainly that was an interesting exchange we had that I fondly remember. When you went to RCA did you go there with your own researchagenda they had approved? No. Well, I came with certain ideas. What did they want you to do? How did this process work? They gave me an offlce and told me to work on whatever I wanted. Oh, that's it? Yes. Herold explained to me later that when he hired people his interest was in how good they were at whatever they had done previously. What field it was didn't matter to him. His concern was only for the quality of their work. His next question would be, "Is this person interested in working on the problems that I can offer?" If the answer was also positive, he would take the person. He would rather take an individual like that who had no idea about the fieid than somebody who had previous experience in the field but did second rate work. That's interesting. He explained to me. "Listen. In the environment of our fab, the kind of people that I hire like to communicate. If I put them into this lab they are sitting in an intellectualfeedback loop, where they cannot help but be influenced in being directed towards the topics in which the lab is interested. They are not going to go off on a wild tangent." I would have been permitted to do so. In fact later on I did go on a fairly wild tangent, but even then it was encouraged on the grounds, "Well, maybe something will come of it." i see. In a place like this where people were allowed to do what they wanted to do, within I gather rather broad constraints. how does accountability work? How did they decide whether to keep people on and determine whether people are good or not good? By the results? Basically people were judged by the quality of their work. And it was encouraged to go out of the established conventionalwisdom. Was it a healthy environment where failure was encouraged? If you tried and failed was that not seen as a negative thing? In some places that would be treated as a very negative thing like, "That's terrible. We don't want that." No. I think failure was encouraged. I remember when I was working on a particular project, I was working very hard and it eventually became clear to me that this was not going to work. It had been clear to others long before that it wasn't going to work, but there was no influence on me. I do remember one day in the morning I drew my conclusion that it was not going to work. I cleaned up my workbench, cleaned up my desk, went to my supervisor and said, "Harwick this is not going to work. I'm going to change subjects." He said, "Yes? Well, that's fine. We knew you would come to that conclusion." That was it. There was no pressure. It was an experience. Of course I was the kind of person who was willing to drop the subject. There are sometimes people who do not want to let go of it. The dumbest reason for continuing something is because you have made the mistake of starting it. I have always been willing to drop projects. In fact I have never been interested in milking the last bit of juice out of something. If I had succeeded in achieving the key point, suddenly I would discover I had lots of friends who were willing to do the rest. Why not let them do it? Did you have an opportunity at RCA, the kind of problems, to go back to heterostructure bipolar transistors? Actually that is something I did try to do. In fact that was the project I decided to drop. The technology was staggering, the equipment primitive. And remember, by that time I knew more metallurgy that most theoretical physicists. So I came up with the idea of putting a sillcon/germanium alloy on a germanium base. This was all on germanium bases. How do you do this? I knew my phase diagrams quite well, so I made a silicon-gold eutectic. Silicon-gold has a relatively low melting point 360°C or something like that. I made the silicon-gold eutectic which is an unpleasantly brittle substance, put it on an anvil and smashed it into a powder, and with a pair of tweezers picked up little grains and put them on the germanium wafer and alloyed it at 500 or 600"C, the eutectic would melt, it would eat up germanium and the germanium would then recrystallize.And we had added some dopants. You did this yourself? I did the experiments. I didn't have a technician. I did all of this myself. My one complaint at RCA is that they did not give me a technician. I think they had the right instinct. I didn't know how to use a technician. That must have taught you new things trying to do this stuff yourself. Yes, yes. This is where Lou Pensaks advice on how one does things came in. We actually made some transistors, but it was clearly a technology that would never amount to anything. So this is that and I dropped it. At that point I decided to get out of transistors and move to something altogether different That must have been in late '56. I did write two papers, and those papers played an important role. I then became very much interested in hot electron transport at low temperatures -which is something totally different. When you look back at all the work you did at RCA, of what are you most proud? In hindsight I see that those two papers that I wrote clearly had the greatest impact. But I did other things that were at the time certainly important to me. What gave you the most satisfaction at the time? I don't know. I don't want to single out any specific things. Of course by hindsight it's very clear the heterostructurework was the important one. And that paper in RCA Review was probably one of the most papers I ever wrote. I made a mistake by publishing it in an obscure journal, with the result that no one read it. However Zhores I. Alferov, the Russian with whom I won the Nobel Prize, read it. He knew the paper.
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I see. I would have imagined that the RCA Lab's journal would have been read by a lot of people just like the Bell Labs' journal. That was RCAs idea. The RCA Review was sort of an imitation of the Bell System Technical Journal, and it never really acquired the same following. I see. It turned out to be a place where a lot of papers were put if you couldn't get them published elsewhere. Did you think this was an important paper when you were writing it? This is hard to say. In that paper I clearly spelled out the heterostructure design principal. If I were to rewrite that paragraph that I quoted in both my Nobel lecture and elsewhere I would clean up the English a little bit, but the idea is clearly there. I realized the power of the idea. What was not clear to me at all was how important the idea would become. The real triumph of this idea is the heterostructure laser, which draws exactly on the concepts that were outlined in that RCA paper. Incidentally, this is something very typical that the fruitfulness of a new idea will not come until later. Right. There is a wonderful ouote bv David Mermin in Phvsics Todav a few vears ago. He says something like L you have to look udthe exact Lording-"I'm looking forward to the day that people realize that discovery does not work by deciding what you want and then discovering it." Isn't that in your Nobel lecture? I quoted that in my Nobel lecture. This has implicationsfor those who say funding for science should be based on what the applicantThat is total nonsense. Is there anything to be gained by trying to get scientists thinking about problems that have some obvious need and utility in society? In other words even in theoretical issues like attacking an important problem and applying good science to it? This flows two ways. On the one hand Deoole who have Droblems that thev want solved can and should try to get more fundamenta1:orientedpeople ' interested. I think we all acknowledge that one. However on the other side and I can only speak for myself - I have always been interested in fundamental principles, but whenever some conceptual advance had been made I have also always asked myself, "What could be done with that?" I did not restrict myself in my explorations to things where I saw applications beforehand, but I periodically asked myself, "What kind of applications might this have?" Sometimes I could outline some and sometimes and I could not. And if I could not, I still went on. It didn't stop me pursuing a certain thing. You gave applications some thought. I always gave it some thought. Critical thought. One has be honest about it and not come up with something where a few more minutes of additional thought would show it to be nonsense. I think you spent three years at RCA Labs. Yes. Then you returned to Germany to head up the Phillips Semiconductor Group in Hamburg. That's right. After reading some of the things you wrote, I was wondering if being homesick was one of your reasons for returning to Germany. Yes. Was there something more to it than that? No. It was simply homesickness - on the part of both my wife and myself, though more my wife. Is your wife German? She is from Berlin. We never discussed when you met your wife. I met her when I was a student at Gottingen. Okay. So she was homesick to get back. She must have left Germany with you almost immediately. She followed me after a year. She stayed behind because we had a young child. She stayed behind with her parents. Then she followed me, but then she was terribly homesick. And Iwas offered what looked like a rather attractive job at Philips. So I went back. I must say that I have nothing but good things to say about the Philips Company. They treated me wonderfully. What was the undertaking? They had a new research laboratory in Hamburg - a lovely city incidentallyand I was the head of the semiconductor group. I decided to steer this group towards gallium arsenide. That was in 1957. I got the people in Eindhoven who were a bit astonished and saying, 'Yes, why not?" One person was assigned to do this technology. When I decided to go back to the United States this project was shut down. Why did you leave? Were you unhappy with the way things were going there? I had no problem with Philips. Germany simply was not the same. Our perception of Germany changed. What does that mean? My wife and I both suddenly realized that we wanted to go back to the United States. That was basically it. Philips tried all sorts of things to get me to stay. They were very nice about it. It was a reverse homesickness. You had to leave the U S . to realize that you wanted to return to the U S Yes, so I book this under mental health expenses. Did you think you did anything in terms of your own professional development or ideas in physics there? While I was in Hamburg? No. Nothing. That must have been a disappointing time for you professionally. Well, I did some thinking and I think I wrote a couple of theoretical papers, but it does not show up in my productivity resume. You came back to the U.S. and Varian Associates. Why Varian?
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I knew the head of central research at Varian, Lou Malter. I knew him from RCA. And the people at RCA actually wanted me back. Oh, they did? Yes. I don't really quite know why I didn't want to go back to RCA. I asked Lou Malter a little and he said, "Oh yes Sure. Come." And we never agreed what I would work on. You never did? We never talked about it. He said, "Just come. There are plenty of interesting things around." He knew me well enough that he realized it would probably work. And I spent several years then at Varian Associates trying to build up a semiconductoractivity there. You were ooing the diode laser, right? Well, this is how the idea came about. I was actually not allowed to work on it. Yes, I wanted to get to that. How did you come upon this topic? I had worked on what we now call heterostructure bipolar transistors. And you put it aside for a while. I put it aside, yes. I think it was in 1962 at the Device Research Conference in Durham, New Hampshire, which was the big annual device meeting, that all hell broke loose about semiconductor lasers. The first gallium arsenide laser was reported and that dominated the conference. And I really wasn't interested in those things. I knew that the theoretical principle permitted that and i was still astonished that it actually worked, but I was totally occupied with something else. But a colleague of mine, Sol Miller, was also at that conference and he took a deep interest in it, and so he started working on that one after we returned to Varian. And it must have been in March of '63 that Ed Herold, who had come from RCA, the director of research at Varian. Ed Herold from RCA? The same Ed Herold. Lou Malter had hired him too. He was the director of research? He [Herold] was not director but vice president of research. Anyway, he insisted that things get done RCA style, and that included weekly colloquia. Therefore all of us had to give talks - which i think is a good idea. Sol Miller was asked to give a talk and he picked that laser topic. He gave a beautiful talk pointing out all that had been done and also that these things didn't work at room temperature and didn't even work continuously. It required very, very short pulses, and certainly a low temperature had to be used.
At the end of the talks Herold said, "That's all very nice, but what are the chances of getting this to operate cw and at room temperature? Because that's where the applications are." And Sol Miller replied suddenly something to the effect that, "No, this has been looked at." Then he quoted some paper. I do not want to repeat the quote, but the quote said that this was fundamentally impossible. Fundamentallyimpossible. Ed Herold was not about to put up with the statement that something was fundamentally impossible without explaining why it was fundamentally impossible. Then Sol basically gave an explanation that boiled down to that, "You first of all need a population inversion, so you need a degenerate doping on both sides, and if you bias it to the point that you actually get stimulated emission the electrons leak out to the p-type side very, very rapidly. Holes leak out to the n-type side.'' You can't maintain the population inversion? You just cannot get a decent population inversion except at low temperatures where the statistics is in your favor or pulse where you have transient effects. And I do not know whether Sol Miller was finished, but I certainly said, "That's a pile of crap." In those words? In those exact words. All you have to do is put a wider energy gap on the two sides. It was obvious. The moment I was told that there was a problem the answer was obvious because at that point I had been thinking enough about heterostructures Anyway, everyone was astonished and we did a number of things. I wrote a paper on this one and submitted it to Applied Physics Letters. Yes. They rejected it. Before you go on, do you have any idea why it was rejected? All of this correspondence got lost. Do you recall? I do not remember exactly why. Ed Herold, who was a big shot in the IEEE, did not like the idea that I had submitted it to Applied Physics Letters in the first place. "Well, send it to Proceedings of the IEEE They will publish anything." That is of course why I hadn't wanted to send it there. The letter section there was not very good in those days. Do you think that was why that paper was ignored? I submitted it, it was accepted, and it was published. No one read it. A reviewer had pointed out to Panish and Hayashi, who subsequently did this, that this paper of mine existed. When they published they were gentlemen and acknowledgedthe idea. And we wrote a patent. Yes. That patent was assigned to Varian, wasn't it? Yes. It has safely expired. We wrote a patent. I wasn't allowed to put a band diagram into the patent because the head of the patent department was an electron tube man who did not understand semiconductors. He wouldn't put anything into a patent that he himself did not understand. Oh my goodness. He argued however that science really does not matter: all that matters is that the correct prescription of what to do is given. For a patent, yes. That is technically correct, but if you look at Bill Shockley's patents there is always a very explicit elaboration on the science.
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Was your work in this paper purely theoretical? Purely theoretical. There were no prototypes, no fooling around with experiments, it was all theoretical arguments? It was all theory. And in fact it wasn't at all clear how one would go about building one. We didn't really have the technology. We got a number of criticisms. There were a few people who said, "Your physics is wacky. It doesn't work." But that wasn't really what bothered me. I had been through this sort of mode of operation before and had learned not to pay attention unless everybody tells me that it does not work. I prefer to rely on my own judgment. I was convinced the physics was right. The other argument of course was, "There is no technology." And that was true. But then came the killer. That was, "There is no point in developing the technology because this device will never have any practical applications." End of statement. Was that the reason why Varian did not want to pursue this further? That's why. They didn't say, "It's not in our business field." They said, "It has no applications." Did you fight this or did you give in to it? I gave in. I probably would not have given in if the Gunn effect had not come along at the same time. What is the Gunn effect? The Gunn effect is the phenomena where if one takes a piece of gallium arsenide. applies a high voltage, then under certain conditions high-frequencyoscillations result. That was fascinating physics and I was the first to offer an explanation for the Gunn effect. I worked on that for a number of years. That was my consolation prize for not having been able to work on the laser. Well, I should not say consolation prize. It was sort of an alternative since I could not work on the laser. And we had the technology for the Gunn effect. In a way of course this is regrettable, because as a result of this work I never played any role in the subsequent realization of the DH Laser. Is that a source of disappointment for you? A little bit, yes. You also mentioned that as an alternative to this rejection of the laser rekindled your longstanding interest in high-electron negative resistance effects. This is the Gunn effect. I see. But you had worked enough for your doctorate dissertation in this broad area. In the broad area, but the Gunn effect is something quite different. Okay, but you say "with a longstanding interest in this." I had a longstanding interest in transport properties under obscure or unusual conditions. In mv dissertation I worked on hot electron ohenomena. During my last year at RCA I was working on hot electrons and'hot holes in germanium. One of the reasons why I became interested in gallium arsenide was because theory predicted that the thing that we were looking for in germanium would be much easier to find in gallium arsenide. Okay. That influenced me in starting a gallium arsenide project. Then I went to Phillips, and we wanted to look at high field transport properties as the first application. We did not have transistors or lasers in mind. Typical for my kind of thinking, I was simply convinced that the three-five compounds held a tremendous amount of future promise. So let's be amongst the ones to do it. Did you go to Phillips and pursue this idea of transport issues? That's not why I went to Phillips. I wanted to do something that they were not doing in the main lab in Eindhoven. And I wanted to do something that was at the forefront of solid-state technology. I wanted to get into compound semiconductors and I wanted to work with gallium arsenide specifically. You spent ten years on research and engineering around the Gunn effect Would that be where your biggest theoretical accomplishmentslie? I certainly have more papers in that area than in anything else. It was a significant accomplishment. I would say I was one of the handful of leaders in this field from day one, and it was only when I came to Santa Barbara that I put an abrupt end to it. I decided to do that. Was your Nobel Prize award related to the Gunn effect? No. It was for the development of heterostructuresfor high-speed- and opto-electronics. Thinking back, do you think the reason they gave this science such a high significance was because of the practical technological effect it has had? Absolutely. And that if that hadn't happened they probably would not have given you that award? Absolutely. Yes. The 2000 Nobel Prize in Physics really was a break with the tradition. The tradition for ninety years had been to award the prize only for discoveries, even though Nobel's will specified discoveries or inventions. There are certain reasons why the restriction to discoveries was made around the time of World War I. Why was that? It probably had to do with the Nobel Prize for Gustaf Dalen in 1912 which was purely a technological invention. That caused a great deal of protest. Many felt that the Nobel Prize in Physics should not be for something like this. If one simply looks at the Nobel awards, they are almost all for discoveries and those that were inventions were typically inventions essential for research discoveries. Right. Okay. The bubble chamber is a good example. Instrumentation.
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Instrumentation.So when friends and colleagues mumbled about me getting it someday, I looked at the statistics and took the attitude, "Well, they do not know the rules of the game." That was probably good for my mental health not to take those comments too seriously. Then, since people had been talking about it I sort of was thinking about the possibility and thought to myself, "Well, they are not going to give it to the HBT. They are not going to give it to me for the laser. I may have been the first one to spell out the idea, but I did not do the first laser. If however they decide to give it for the heterostructureconcept, then I have a chance and I will probably share with Alferov." You said that to yourself? Yes, I said that to myself. I never talked about this to anyone. I think you are the first one to whom i have told this. And this is of course what happened. But it was clearly a break with tradition. But yours is less of a break than it was for them to give it to engineers like Jack Kilby. Yes, for Kilby it was even more so a break with tradition. However I think it was well deserved. They must have gone back to read Nobel's will. Okay. I want to cover some more ground before our time runs out. I am very interested in your interpretation of Moore's Law. You gave a plenary talk called "Speculations about Future Directions." This must have been the MBE paper published last year. All right. In it you say, "Moore's law reflects the triumph of parallel assembly." Yes. Would you please elaborate on that? "Moore's law is an observation; it's not a law. Of course. Yes. It is an observation that spans several decades. The number of devices, per chip and per processing step processed in parallel has increased exponentially or approximately exponentially. In order to be able to do this a reduction in dimensions was necessary. But the reduction of dimensions was an enabler. If the dimensions were reduced and then these devices were done serially, one at a time, then you would not have Moore's Law. This is not going to make a Pentium type chip doing one device at a time. This is my perspective on Moore's Law. In that sense it is a triumph of parallel assembly. I raise this issue periodically whenever people say, "As the dimensions get smaller quantum mechanics will become more important. We will build a quantum device then. Once we have a quantum device Moore's Law continue for a little bit longer." But actually quantum devices are all put together serially. Aha. That's your point. This is the wet blanket that I put over the subject. Moore was extraordinarily perceptive, because he didn't formulate it this way but he realized the trend and that we were veN. very far awav from DhVSiCS limitations. In mv ' perspecttve Moore s.Law was based on the development in the InfrastructLre If one asKs "Why oion t we 00 it right away?" that is a very easy question to answer there was no infrastrLcture instrunentation manJfactLring an0 there were no crystals of the proper perfection m nterested in tnis in my own research Someone to10 me that Moore s Law is essent ally a scaling up is%e - not indefinitely out one can scale up in this way A straigrlt line cannor be orawn on log-paper forever Yes B L I~ha0 tne impression that one of the reasons it rea ly too6 off was the emergence of CMOS that CMOS tecnnology is geared to this ulna of th ng whereas bipolar is not Yes that s true Let's p ~it tth s way Take cadse and effect the other wdy aroLno it s only with CMOS inat we coulo do it And of c o m e Moore preaictea CMOS I m mteresteo in the relation with bipolar technology The principal reason tnis COLIO not be oone with oipolar is that thermal load is JnbearaDle Eipo ar is a hot plate Okay B polar cannot scale up the way CMOS can No I see Bipolar is obvioLsly very very impcrtant Your cell phone is loaded with bipolar Certainly on the transmitling sloe it's bipolar Probably nBT IS on the transmitter sode an0 it may be HET is on the receiving side I was lh nking ,n terms of computer development became at one point a bipolar was a dominant form of device in processors Yes E g mainframe compJters Lseo to rLn on ECL Emitter Codplea Logic Yes Ano tnere is not a oevice that generdtes more heat per fJnction than Emitter Coupled Log c I'm writing a book now Control Data Corporation and they were so weu 10 the oipolar because of the speeo aovantaye they had Yes They ha0 a speeo advantage bt.t that advantage is gone Cray didn't stop using bipolar Lntil tne late 1990s Yes And of c o m e as the devices got smaller they got faster too For someone who is not in the field, does the valde of the mooel of neterostructLreshave an eqLal technological importance for the CMOS oevice? No At least I do not see it I think there is a goo0 reason why CMOS ContinLes to be silicon though we may see silicon-germaniumin silicon technology I know that many of the s licon houses are working on silcon-germanlam technology thoLgh l o o not know any details In tnat sense that is heterOStrJctLre One of the traoitional explanations for tne r se of silicon was its importanceto the melitary in terms of its stability to oamage Yes I
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And that is the reason that silicon can dominate more than germanium. Certainly the military were the ones who initially supported it and helped it get off the ground, but I think what was probably more important was organizations like Bell Labs that realized that germanium was too limited. Too limited in what respect? Temperature capability, processing capability. Jack Morton probably did more than anyone else to promote silicon technology early in the game when it was still largely bipolar. Then of course there is the importance of that oxide. Silicon is a rather unusual material. All the attempts to imitate silicon in compound silicons have in my opinion been a waste of time. They fail to reallze that silicon is the abnormality. It's not the rule but the exception? Not the rule. It's the exception. It has that wonderful stable oxide which serves for protection as a masking aid, it has a good thermal conductivity and it has the right kind of an energy gap. You can't find that in the other materials? You do not find this in anything else. It has a lousy mobility. That was the principal reason we thought silicon would never fly - the mobility. I remember back in the days at RCA we didn't believe in silicon. First of all one could not get rid of that stupid oxide. And certainly the mobility is still lousy. This is why we believed in germanium. Oh, I see. That was wrong of course. Do you think there are any limits to the switching speeds of bipolar transistors? Have we reached the limits? You will have to ask my colleague, Mark Rodwell. He is the leader on this one and he expresses things in terms o ,,f which is not the same as switching speed. Of course typically it is not useful to switch applications anyway. And his F-maxes are so high that he does not measure them. These are extrapolated figures. You left Varian in '66 and joined the University of Colorado in '68. That's correct. That leaves a two-year gap. What did you do during those two years? Were you a consultant? I was at Fairchild. That's not in your biographical sketch. Yes. Those were two very unhappy years. Why was that? I do not want to talk about it. All right. You were in a silicon world? I was a misfit in a silicon world. They were unhappy years, but that did not in any way influence my good relations with Gordon Moore. Okay. That explains why you went to the University of Colorado. You wanted to get out of Fairchild. Yes. This was the first time you worked in a university. After all those years in industry or relating to industrial people, what was it like to come back to academia as a physicist? I enjoyed it. I was a bit concerned about being on a fixed schedule, at least for teaching, but the intellectual freedom that one has at universities is just wonderful. Okay. Were there any attitudes in the industrial environment that you would like to have found in the academic environment? No. What did you do at the University of Colorado that is significant in your mind? I went there in '68 and was still very heavily involved in Gunn effect. I was also doing a number of theoretical pieces of work, though I didn't really do anything terribly important at that time. The Gunn effect work was good work, but the best part of the Gunn effect was done already while I was still at Fairchild. That is in fact something that I did at Fairchild. I started working on the Gunn effect at Varian and a couple of my most important papers on that subject were written while I was at Fairchild. Actual publications? Yes. They are under the Fairchild byline. And I continued to work on the Gunn effect at the University of Colorado but it was getting into increasingly subtle details. When I came to UCSB I decided, "That's it." When you left the University of Colorado to go to Santa Barbara you insisted that they choose a specialty in which they could realistically be successful rather than being like all the others. What was that about? Yes. I had an interview at CU with Ed Stear. We had a long discussion. He was at that time chairman of the department here at Santa Barbara. He had heard that I was interested in returning to the west coast so he visited me in Boulder. I knew a little bit about UCSB. They had a very, very good silicon technology teaching lab. But I wasn't at all impressed by the research they were doing. When Ed Stear visited me in Boulder he said, "Well, you know our solid-state laboratory," and I said, "Yes." He asked me, "What would you do with this laboratory?" Ivery quickly forgot this was a job interview and said, '"Wellsure as hell not what you are doing." He acted very upset and asked, "Why? What do you mean?" I criticized their research work. So this led to a horrible, unfriendly discussion for a while. I had decided what the hell. And then at one point he looked at me and said, "Oh, shut up." I thought, "Well, all right. He doesn't want to hear what I have to tell him." But very quietly he said, "Herb, I am looking for someone to rock the boat. You sound like you are my man. Back to my question. What would you do?" So I said, "All right. I know what everybody else is advising. Everybody is advising you to get into the mainstream silicon technology. Don't. It's too late. It's too expensive. And most importantly, the graduate program depends on being able to attract top graduate students. You will not be able to do this one and they will all go to other places."
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Right. I said, "My own interest is in compound semiconductors. I think this is going to be an important field. Different from silicon. It's not something in which everyone has to be involved. This discussion took place in the fall of '75. At this point there were three universities that had critical mass -critical mass meaning more than two professors. Stanford, Illinois and Cornell. There is a place for a fourth. If you are willing to put all your eggs in one basket and you are going to gamble, you have a 50/50 chance of making number four. If you go into silicon technology you have a 100 percent chance of being an also-ran. And that still was going to be a gamble. So that's what we did. We still don't have any silicon technology. That's what actually brought you here. I was basically the one who set the strategy for this concept. I see. Okay. In terms of your work here, what interests and fires you now? Well, it's a variety of things. My most recent papers have been on superconductor-semiconductorcombinations basically taking an indium arsenidelaluminum antimonide quantum well that is heavily modulation-doped, so that there are large electrical concentrations in the quantum well but still very high electron mobility. Okay Then on that indium arsenide is put niobium electrodes Indium arsenide has the fascinating property of not making Schottky barriers. so these are true ohmic contacts. Down to 9 Kelvin these are simply ordinary resistors. Then as soon as the niobium becomes superconducting the conductivity properties of the indium arsenide itself change. Eventually you have a form of induced superconductivity through the indium arsenide. That's a fascinating phenomenon. What are the theoretical issues that interest you in that? The theoretical issues are that we don't understand the details. We do not understand the temperature dependence. I think we understand the basic physics that is behind the electron transport. It's a phenomenon called Andreev reflections that Dlavs an imoortant role. Others have studied Andreev reflections, but /n &her systems the transport is diffusive. In other words the diffusion process, how the carriers get from one electrode to the other. Right. And the indium arsenlde is ballistic. Ballistic? Yes. Therefore we are building what in the jargon would be called ballistic weak links. That topic is still fascinating. We have done quite a bit of experimental work here, but that was basically finished in around '99. It was finished when the Office of Naval Research pulled the rug. How much of your funding comes from the defense- and government-related work? At that point my ONR funding was the basic money. I have done other work under industrial funding. How does one sell that kind of research to ONR? You would have to ask ONR why they cancelled it. Okay. They initially supported it. What did they see in it? Obviously they saw something as being useful for them initially. I do not know whether the original reason for funding it had anything to do with utility. ONR has a strong tradition in supporting things that are quite fundamental. I never made any promise for an application. I simply felt it was a sufficiently crazy phenomenon that it deserved study. That was my last major experimental project here. A couple of Ph.D. dissertations came out of that. I am fascinated by Kroemer's lemma on new technology A lot of people quote it in one form or another. Yes, because I've been citing it often enough now. It was originally formulated at a NATO Advanced Research Workshop in France. For the purpose of this transcript let me quote it here. Let's see if I got it right. "The principal applications of any sufficiently new and innovative technology always have been and will continue to be applications created by that new technology." And the emphasis is on the word created. What prompted you to come up with this and how? What prompted me to come up with this is that, particularly in engineering research projects, too much emphasis is put on the applications that can be envisaged. But in the really big stuff the applications are always created. The computer was created by silicon. The portable computer was created by liquid-crystal development. Was this a defensive move on your part? The laser created the compact disc and fiber communications. Obviously you came up with this to counter some other perception. Absolutely. Yes. Which has funding implications. I grew up in a research environment where you were quite free and it was not difficult to get funding without having to promise immediate applications. To a large extent that has disappeared. Even in universities?
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In the funding for universities, yes, particularly on the engineering end. I think physics doesn't see that to the same extent. If you realize that any sufficiently new invention or discovery the principal applications always have been created, then you understand the importance of this type of research. in addition. the creation tvDicallv haDDenS throuoh somebodv other than the original researcher. It cakes a diffeient kind ormentality. litakes somebody who says, "Hey, this is an interesting discovery. I know exactly what to do with it." If the researcher himself must tell the potential funding organization the applications, then progress is actually being restricted. It is not being advanced. That's a good point. That is what I keep hammering on. The Nobel Prize has helped me in getting a few more people listening to that. Yes. A certain credibility grows around you now. My success was basically achieved by following this principle. I never gave a damn what the applications were. I would ask myself what might the applications be, but that did not control what I was doing. Right. I see. Another lemma of yours is the proof of ignorance. Kroemer's lemma of proven ignorance. "If. in discussing a semiconductor problem, you cannot draw an Energy Band Diagram, you do not know what you are talking about." Did you formulate this lemma expressly for your students or for colleagues? it was not formulated for anyone in particular. Why was there a need for this? How did you come up with this? Because I have seen it too often that people cannot draw Energy Band Diagrams, and in reality those same people do not understand how things actually work. I really do feel that knowing how things work is absolutely essential. And without Energy Band Diagrams one does not understand heterostructures. I had this in my Nobel lecture. There is also the corollary that, " I f you can draw it but don't, then your audience won't know what you are talking about." The students are always chuckling. If someone gives a talk and doesn't draw an Energy Band Diagram they know Herb Kroemer is going to raise the question, "Would you please draw an Energy Band Diagram?" And my colleagues agree with me. They absolutely agree with me. This would be something that perhaps would be something to apply to engineers working in the area who might be tempted to discuss things without ever going back to these first principals. That's right. Engineers are particularly prone to not doing Energy Band Diagrams, but they are not the only ones. Pnysicists will do it too? You will find this among physicists too. Interesting. I have one last question for you. In generations to come some young physicists will look to the greats for a role model and some will choose you. What traits do you hope they will try to emulate? You chose Niels Bohr for certain reasons. Why would you like them to see in you as a physicist? That's hard to answer. One of the things that made me tick, certainly skepticism towards what authorities say and a deep interest in really understanding on a fundamental level what I have done. These are probablv the two important things. I want to thank you very much for a most fascinating interview You're welcome.
Not Just the Blue Sky 99
Copyright 2002 IEEE. Reprinted, with permission, from TekIa S. Perry, "Not Just Blue Sky," IEEE Spectrum, June 2002, pp. 32-27.
rofessor Herbert Kroemer
An unusual condition was imposed on Herbert Krocnicr at the start of his research career 50 years ago He was not allowed to touch anything in his workplace, the Telecommunications Laboratory of the German Postal Service The fear was that this recent graduate in theoretical physics would break something Far from constraining him, the restriction expanded his horizons With just pencil and paper, he began sketching out theories that would resonate across the entire world of semiconductor science And that work would culminate in a Nobel Prize in Physics in 2000 and this year's IEEE Medal of Honor, the iatter for "conwbutiors to high-frequency transistors and hot-electron devices. especially heterostructure devices from heter0s:rLct Jre bipolar t'ansistors !o labeis, and their molecLlar beam epitaxy :ethnology " Wnile his theories led to produc!s that earned their manufacturers billions of uollars, none of tne profits came to Lroemer "That really uoesn't bug me." he says. sitmy in his small and sparsely decorateu office on the Santa Barbara caTpJs of the Lniversity of California, where he is now professor of elecirical and computer engineering ano materials IEEE Fellow Kroemer never trieu to aevelop appllcations of his work--or even preuict them 'I like lemmas," he told IEEE SpectrLm. "and this one about applications is perbaps my most imponant message It's called 'The futility of predicting applications, and states 'The prircipal applications of any sLfficiently new and innovative technology a ways have been a r o will contime to be applications crea!ed by that flew technology ' ' So he doesn't begrudge o!hers the frults of his ideas. "I've always calleo myself an oppor:t.rist." he says "This is supposea to be a derogatory term, bur I'm not one bit ashamed of accepting opportunities In the scientific sense, I "as an o ~ ~ o r t ~ vvho r ~ i nas bl looking for challenging problems "
l u o r r i n i i y ii!,,fs In histi school in Gerrnary, Kroemer played aruunu with chemistry experiments out soon turned to physics "1 likeu the beautiful logic of a structure witn a relatively small nLmber of fundamental principles from which you codd draw far-reacniiig concltsicns," he says A uriiversity cheniistry course tnat reqirirea rote memorization of lists and lists of chernical reactions destroyed any remaining ir!eres! iri that science College Has a breeze. He entered the University of Jena in East Gerrnany if1 1947, then left for West Germany the next year uurmy the Berlin airlift and was accepted at 'he Univers#tyof Gott ngen. Four years later he received his Ph D for a theoretiml dissertation on germanium transistors that discLssed electron transport in high electrical fields It broke little new gromd. ana he takes no particular
Not Just the Blue Sky 101 pride in it. He explained some experiments, he says, but the explanation later proved completely wrong. As he told Spectrum, his actual knowledge of the subject matter was rather limited. But what his research advisor really cared about was methodology. Does a student know how to tackle a problem with no background in the subject? And does he or she know how to acquire the knowledge needed? And that Kroemer knew how to do. To this day, his view of education is that accumulating methodology matters more than accumulating knowledge of subject matter. "It was not until a number of years after working with him that I realized how unique this is," says William Frensley, a one-time graduate student of Kroemer's and now professor of electrical engineering at the University of Texas, Dallas. "Other students worked for professors who were specialists and became specialists in the same thing, whereas we said we have a problem, and we are going to master whatever techniques it takes to solve it."
Postal service In 1952, when Kroemer received his PhD., an academic career was out of the question. The lines of succession at existing German universities were long, and no new ones were being established. So he joined the Telecommunications Research Laboratory of the German Postal Service in Darmstadt. This is less of a stretch than it seems. The postal service ran the telephone system and had a small semiconductor research group--some 10 scientists-in its telecommunicationslaboratory. That group hired Kroemer to answer any theoretical questions that arose, to give talks on any subject he thought relevant-and to keep his hands off the research equipment. "1 enjoyed this thoroughly," he recalls. For one, he had liked the role of
teacher since high school, when his physics teacher asked him to prepare and deliver a lecture to the class. For another, being at the researchers' beck and call presented him with a wide variety of problems in diverse subjects. In solving one of those problems, he went against the conventional wisdom of the time. Researchers were developing pn junctions of indium and germanium. They did this by depositing a layer of indium on a layer of germanium, then heating the structure to form the pn junction. Kroemer was trying to understand how exactly the junction formed. Obviously the molten indium dissolved some of the germanium, and the belief was that it diffused into the germanium beyond the layer in which the germanium dissolved. But Kroemer concluded that the process was one of recrystallization--theheated indium dissolves some of the germanium, and then upon cooling the germanium precipitates out and recrystallizes, incorporating some ofthe indium atoms, which replace some of the germanium atoms in the lattice. What he didn't know was that researchers in the United States, at General Electric Co. and RCA Corp., had simultaneously reached the same conclusion. But what he did know was that to be at the research forefront, he needed to leave the German Postal Service and get to the United States. He started looking for a way to get there. Researchers from other countries occasionally visited the lab in which he worked, curious about this small semiconductor research group. In 1953 one visitor was William Shockley. then at Bell Telephone Laboratories. "1 spent about two hours with him," Kroemer said. "We were having a marvelous time. I told him about the work that I'd done for my Ph.D. dissertation, and about some of my ideas of how to make transistors fast by putting an electric field into the base. He seemed intrigued by that." Kroemer asked him about coming to Bell Labs, but Shockley, as an official visitor, told Kroemer that he would have to go through official channels, starting with informing Postal Service management of his intentions to apply for a job in the United States. The young researcher was so grateful for the job he had at the Postal Service that he was "terribly squeamish about telling my management that I wanted to leave." Later in 1953, the Darmstadt lab had another U S visitor: Ed Herold from RCA. Kroemer asked him whether RCA was working on npn transistors (back then pnp transistors dominated). Herold was guarded in his responses: but Kroemer guessed out loud what the RCA researchers were doing, what alloys they were using (lead-antimony), the percentage of the antimony, and the alloy temperatures. His guesses proved quite close to RCAs experiments, and the impressed Herold didn't hesitate to offer him a job. (All the same, it took a year for Kroemer to obtain a visa, even with RCAs help.) At RCA in Princeton, N.J., Kroemer did theoretical research on an
102 Selected Works of Professor Herbert Kroemer impurity diffusion process for building transistors. In the diffusion process, the doping of the base region was deliberately graded from a high value at the emitter to a lower value at the collector. Because this gradient introduced a built-in electric drift field into the base, the result was called a drift transistor. The first commercial product to come out of that research--the 2N247-had a high-frequency performance far beyond that of other commercially available transistors of its time. Its power gain cutoff frequency of 132 MHz made it suitable for use in FM radios. While Kroemer was theorizing about how a drift field could make transistors switch faster, he had an idea about grading the basic semiconductor itself. If an alloy of two semiconductors replaced the single semiconductor, it could be given a continually varying composition to change its band gap, which is a measure of the amount of energy required to move an electron from a semiconductor's valence band to its conduction band. This varying band gap would be another way to introduce a drift field into the base, again in order to improve transistor frequency performance. He had mentioned varying a material's band gap in a paper while still in Germany, but expanded the idea and in 1957 published two papers about it, one in the RCA Review, another in the Proceedings of the IEEE.
Theory into practice While Kroemer trusted his theory, he didn't know how to build actual semiconductors using his principles. Building them would require either a base region consisting of a graded mix of different semiconductor materials with varying band gaps or else one material in the base but a different material in the emitter. He tried to build a transistor with germanium-silicon alloy as the emitter on a germanium base. To this end, a gold-silicon blended mixture was alloyed onto germanium at 600 "C, hot enough for the melted mixture to begin eating up germanium, precipitating the germanium-silicon alloy emitter on cooling. Unfortunately, during the cooling, most of the devices cracked. "It was one of those technological blind alleys where you're not exactly embarrassed that you have tried it, but you're not surprised it didn't work," he says. At the end of 1957, Kroemer decided to get out of transistor research. He had no interest in traditional transistors, and heterostructure transistors, with existing material technology, could not be built.
"I promised myself," he says, "that if a new technology for building heterostructures arose, I'd get back into it." Kroemer left RCA in 1957 and returned to Germany: he, and more especially, his wife, was homesick. Becoming head of a semiconductor group at Philips Research Laboratory in Hamburg, he pushed for work on gallium arsenide, looking at what happens when you apply large electric fields to gallium arsenide semiconductors. "I thought GaAs was going to be an important material, so it was worthwhile studying it." Kroemer feels he did little significant work at Philips and, since his wife quickly concluded she preferred the United States after all, in 1959 he went to Varian Associates (Palo Alto, Calif.), where he did a little research on tunnel diodes before turning to other problems.
Back in the heterostructure game Then Kroemer's ideas about heterostructure devices, shelved for half a dozen years, came back to his attention with a vengeance. It was March 1963. The previous summer, Kroemer and a Varian colleague, Sol Miller, had attended the Annual Device Research Conference, at which GaAs lasers had been introduced. Miller was interested and at Varian's weekly colloquium. he gave a talk about the new lasers. Though scientifically fascinating, he said, the devices could only work at very low temperatures and only for very short pulses, and so would never be truly practical. Asked why, Miller explained that the problem was the lack of charge-carrier confinement: at normal temperatures, electrons would diffuse out of one side of the device as quickly as they were supplied from the other side, as would the holes; therefore the electron-hole pair concentration would never become high enough to cause laser action by stimulated emission. Low temperatures suppressed the effect, but only for brief periods of time.
Kroemer disagreed. Based on his work in heterostructures,the solution, to him, seemed obvious--you just vary the device's band gap, putting a narrower gap in the center and a wider gap in the outer regions, so that the electrons and holes would concentrate in the center [see "H.~t~?r~~structur.~s..E.~jilain~d"]. "My reaction was instantaneous," he told Spectrum. '%Themoment somebody told me about the problem, it snapped." He wrote up his idea as a paper and submitted it to Applied Physics
Not Just the Blue Sky 103 Letters, wnere it was rejected Rather than fighting tne rejection he was persuadeu to submit it to the Proceeoings of the IEEE There it *as accepteo. ot.1 orew littie anent on. h e also f,,eo for a patent on the technology lssLed in 1967, it expirea in 1985 Kroemer wanteo to start working on the creation of room- temperature lasers at once, but his superiors at Varian tolo him that sLch a device wobld never have any applications 'This is me classic mistake--]udgng something not by what applications mignt create, but by now it coLld fit into applications we've alreaoy IhoLght of," Uroemer says. The applications it was usefbl for tLrneo out to incluoe fiber-optic communications, CD and DVD players, LED traffic Iignrs. and laser pointers--none of wnich were arobnd at the time. It
Though 6roemer wasn't pleaseo oy Varian's oecision, the Gunn effect, wh ch had .us! been oiscovereo interested him. Tnis IS a phenomenon in which microwave oscillations are prooxeo when a cerlam voltage .s appl ed to opposite faces of a semiconductor. For the next decaoe an0 more, Kroe,ner explored theones of why th s occurred, three of those years at Varian, two at Faircnild Semiconductor Corp (Palo Aito, Calif ), and nearly eight at the University of Coloraoo in Bou.der
Halls of academia Kroemer was happy to move from industry to academia. Things at Fairchild had not gone well, because the company was dedicated to silicon technology and Kroemets interests had long been elsewhere. He looked forward to the research freedom and also to teaching. But he became dissatisfied. "We had hoped to set up a good solid-state engineering graduate program at Boulder, " he says. During the Vietnam War, many students went on to graduate school to reduce their chances of getting drafted. Stanford University typically recruited the academically top 5 percent of graduate students interested in solid-state research, and Boulder drew on the next 5 percent, who were still extremely good. But when graduate enrollments fell after the war's end, that source dried up. '"Ourambitious graduate program would not fly-it was clear to me that Iwould be professionallydead if I stayed there," Kroemer recalls. Word went out that he was open to a change, and in the fall of 1975, the University of California at Santa Barbara, in the person of Edward Stear, then head of its electrical engineering and computer sciences department, came calling. Santa Barbara at the time didn't have a very good academic reputation: what it did have was a well-equipped semiconductor device teaching laboratory. "So, Herb, you know about our laboratory," Stear opened. '"Whatwould you do with it?"
Kroemer momentarily forgot that this visit was actually a job interview. "Sure as hell not what you're doing!" "It was a rather unfriendly and hostile discussion, and Stear eventually snapped, 'Shut up,' *' Kroemer recalls. He figured he had blown any chance of being hired. But then Stear told him, "I'm looking for someone to rock the boat: it looks like you're my man."
Kroemer, Stear tells Spectrum, "speaks very directly. He is honest, but can be sharp with people, too. He is intense and demanding. He can be a difffcult person at times to work with, but people have ended up loving him." In any case, Stear knew that Kroemer could build the kind of program that Santa Barbara needed, and Kroemer was hired.
By the sea Uroemer left for Santa Barbara in the summer of 1976. He had persuaded Stear not to compete with Stanford, Berkeley, and other top engineering schools in silicon technology, but instead to focus on compound semiconductors such as GaAs. He gave Santa Barbara even odds for making an impact in that technology. "You want to be first-rate or absent." Kroemer says. "I promised myself that if a new technology for building heterostructures arose, I'd get back into it" Kroemer convinced a few former colleagues that they should join him at Santa Barbara, and he also convinced the U S . Army it should buy him a molecular beam epitaxy machine. He said at the time that he wanted it for making transistors with a gallium phosphide emitter on a silicon base, a crazy project if there ever was one. It was not enough to put Santa Barbara's engineering school on the map.
In the mid-I980s, however, the chancellor of the university, Bob Huttenback, decided to put all available money into improving the College of Engineering. A new dean was hired, and 15 faculty were added. "We raided Bell Labs," Kroemer recalls. "Today we have one of
104 Selected Works of Professor Herbert Kroemer the best materials departments in the country--and we still don't have any silicon technology." At 73, Kroemer remains a full-time member of the faculty. One problem he is working on concerns the influence of high electric fields on electron transport in semiconductor superlattices (alternating thin layers of two or more materials with different band gaps but similar crystal structures and lattice constants). More specifically. he is focused on a concept, called a Bloch oscillator, which can in theory generate oscillations up into the terahertz range, potentially opening up that frequency range for numerous applications. So far, it has never been satisfactorily demonstrated as a continuously running device. "1 have some ideas, which may or may not be correct, of what to do about it," Kroemer tells Spectrum. He is also looking at the phenomenon of induced superconductivitv in semiconductors, created when superconductingmaterials aie deposited on semiconductors and operated at low temperatures
Tuesday morning, 3 a.m. Of all the honors Kroemer has received over the years, the strangest was the naming of an asteroid after him. (Asteroid Kroemer orbits between Mars and Jupiter.) One honor that he thought beyond the grasp of a physicist who dealt in such a down-to-earth area as semiconductors (compared to those who grapple with invisible particles) was the Nobel Prize. "Oh, my name had been mentioned over the years." Kroemer told Spectrum. But the Nobel Prize is almost invariably awarded for fundamental discoveries, not for applied research, and so I never believed the rumors." The rumors grew stronger in 1996, when Kroemer was invited to give a talk at a Nobel symposium. "I still didn't catch on." he said. "I looked around at the attendees and saw Horst Stormer, and thought he was the most likely candidate of the group. When he received the prize in 1998, I was enthusiastic and didn't envy him at all-after all, my work was applied." (Stormer and two colleagues received the Nobel Prize for discovering that electrons acting together in strong magnetic fields can form new types of particles with charges that are fractions of the electronic charge.) Although Kroemer never believed the Nobel would come to him, he did continue to pay attention to it. On 9 October 2000, the Nobel Prize in Physics was to be announced the next day. He went to bed that evening thinking, "Wouldn't it be funny if I would get a 3 a.m. phone call? But then I said to myself, Stop being silly, go to sleep!" (Noon in Stockholm, when Nobel announcements are typically made, is 3 a.m. in California.) But when the phone did ring shortly before 3 am., his first response was panic--were his children all right? Had something happened to his grandson? His wife answered, and passed him the phone, saying "It's Stockholm." "If my life depended on it, I could not reconstruct the next two or three sentences,'' Kroemer says. Then the caller put a friend of Kroemer's on the phone, to reassure him that it was not a joke, warning him that he had about 15 minutes before the public announcement was made and the media circus started. "At that point all hell did break loose and the phone was ringing off the hook, starting with German news agencies, since I'm German and it was already midday there. I literally couldn't put the phone down." The Nobel Prize in Physics that year was shared by three people--Jack S. Kilby, also an IEEE Fellow, for his part in developing the IC, and Kroemer and IEEE member Zhores I. Alferov, for '"developing semiconductor heterostructures used in high-speed- and opto-electronics." Alferov, working in Russia, had made similar discoveries in parallel with, but separately from, Kroemer; the two first met in 1972 and have since become friends, even though they are, in a sense, competitors. Kroemer's Nobel citation emphasizes the general principle of the heterostructure, not the individual devices. And that suits him just fine, because he has routinely deferred the question of applications. "Certainly, when I thought of the heterostructurelaser, I did not intend to invent compact disc players," he says. "I could not have anticipated the tremendous impact of fiber-optic communications. I really didn't give a damn about what the uses were." "That's not what I do. The person who comes up with applications thinks differently than the scientist who lays the foundation." And Kroemer laid one tine foundation
Reprinted Articles
Reprinted with permission from H. Kroemer, "Zur Theorie des Germaniumgleichrichters und des Transistors," Zeitschr. f. Phys., Vol. 134, pp. 435-450, 1953. With kind permission of Springer Science and Business Media.
105
106 Selected Works of Professor Herbert Kroemer
zeitschrift fiir Physik, Bd. 134. S. 435-450
(1953).
Zur TheorIe des Germaniumgleichrichters und des Transistors". Von
HERBERT KROMER. Mit 10 Figuren im Text.
(Eingegatsgm om 1. Dcscmbm 1952.)
Bei den in den Randschichten vou Halbleiter-Metall-Kontattenhenschenden hohen F d W h sind far den Transport der Elektronen und Defektelektronea (,,& cber") nicht die normalen Beweglichkeiten d g e b e n d , die giiltig sind. wenu der Potentialabfallbugs einer mittleren freien W e g b g e klein ist gegen die thermische Energie RT. In dLrkeren Feldern gelanger! die Ladungstrtiger mit merklicherW@mcheinlichkeit im Bsndinnere, im Grenzfall sehr starket Felder oszilliert ein Teilchen zwischen zwei StMkn mehrere Male im Band bin und her and k o m t dadurch langsamer vorWWS (,,Staueffekt"). DieBeweglichkeit nimmt dann 80 ab, daB die Teilchendichtc proportional zu Feldstiirke und Stromdichte ansteigt. Der Wert der Proportionalit%takanstanten (,,Staukonstante") wird filr die Lbcher zu 2 10s Watt-*abgesC&tzt; fiir die Elektronen diirfte er erheblich Ueiner sein. Die Dichte det gestauten Tdchen kann von gleicher Gr(lDen0rdnung wie die der St8sMkn werden. Daa RandschichtpotentiaI weicht dann erheblich von der einfachen Scxxomsyschen Parabclgestalt ab. Mit dem abgeanderten Potential werden Kenalinien von Ge-Transjstoren and -Dioden benchnet. Bei geeigneter Wahl der singehenden F'arameter ergeben sich bei den Transistoren hohe Wertc? fIIr den Stromvers&kungsfaktor, bei den Dioden das experimentell beobachtete Urnbiegen der Sperrkennliiien.
-
I. Eideitung.
Nach SCHOTTKY[ I 8 blumen sich an der Grenzflache zwischen Germanium und einem Metall die B a d e r des Halbleiters ( W t i g abgeWuzt Ht) ohne angelegte Spannung um das sog. Diffusionsptential,'V bei angelegter Spannung U urn e U V, auf. Es entsteht eine die Elektronenbewegung hemmende, von U abhbgige Potentialschwde, deren Hiihe fiber der FERYGKante (kiinftig abgekurzt FK) des Metalls
+
c Oo= VD +EL
(11
ist, unabhiingig von U (Fig. 1). Infolge der Bildlcraftamiehung des Met& a d die Elektronen wird die Spitze dieser Schwelle urn
A V = E . . Auszug aus einer cbttinger Dissertation.
.
Reprinted Articles
436
HERBERT KR~MER:
abgeflacht (Fig. 2), wobei F die Feldstarke am Ende der Randschicht (Randfeldstarke) bedeutet . Anstatt der statischen Dielektrizitiitskonstante B des HL wurde dabei eine ,,dynamische" DK q < E eingefuhrt. Denn da die Elektronen eine Geschwindigkeitvon 10' bis 108cm/sec haben, und da der Abstand des Maximums der abgerundeten Schwelle iron der Grcnzflache
zwischen einigen lo-' und 10-ecm liegt, kann man bei einer Vorbeibis 10-1ssec wohl kaum mit dem statischen Wert der flugzeit von DK von E = 16 [53 rechnen. Auch hinkt die Gitterpolarisation in der Phase nach, was die wirksame DK IV abermals herabsetzt.
Fig. 1. Rmdschichtpotential. E L und E v sind die Absttlnde des Leitungs- und Valenzbandes des Ilalbleiters von der FcRwI-l>KT fliel3enden Elektronenstromes -.
jrr=AT2e
-
V8
hT
mit
A=
-
4nemha hJ '
(4)
107
108 Selected Works of Professor Herbert Kroemer
437
Zur Theoric des Germaniumgleichrichters und des Transistors.
Irn Fall der einfPchen ErschGpfungsrandschicht mit der Storstellenkonzentration No gilt nach SCHOTTKY [I31
Daraus folgt mit (3) und (4) fur eU>>VD j,,= A T gexp kT
Solche im (lgj/&, U)-Diagramm geradlinige Kennlinien wurden z. B. von SEILER [I21 an Si-Detektoren gefunden. Aus der Steigung der Geraden 1aBt sich rtickwarts No/va bestimmen. SEILER,der mit V = E rechnete, fwd so Werte fur No, die bis zu einer Zehnerpotenz uber anderweitig bestimmten lagen. Wir sehen darin eine Bestatigung unserer Vermutung q < 6. Bei der Herleitung von ( 5 ) wird die Annahme gemacht, daB die Dichte der fUr den Stromtransport verantwortlichen Ladungstrager, die im HL-Innern mit der der ionisierten Storstellen iibereinstimmt, gegen die Randschicht hin auf einer kurzen Strecke praktisch vijllig abklingt, so daO in der Randschicht nur mit der Ladungsdichte der Storstellenionen zu rechnen ist. Wie im folgenden gezeigt wird, ist diese Annahme qur bei nicht zu groBen angelegten Spannungen richtig. Wird jedoch die Randfeldstarke hinreichend groB, so wird die effektive Tragerbeweglichkeit in der Randschicht so stark herabgesetzt, daB die Tragerdichte stark ansteigt und schlieBlich von der glcichcn Griiflcnordnung wie die der Storstellen werdcn kann. Mit der hierdurch hedingtcn abgciiti clvr t ( vi 1< ;I t I 11 I 1. t ( 1 1 I t 1 rlw 1 i1 - t I f w i r( I die Berechnung der Erschdpfungsrantlsct 1 irli I wit*(l i s r 1 1 1 )I t 11 11(1 itllSchli(:Bend auf die Berechnung von Dioden- uncl -1'r;in~istorkcnnlinienangewandt werden. 8
11. Der Staueffekt. I I , 1 . Transportgesetze k schwachen und starken Felderlt Die Transportgesetze fUr die Ladungstriiger hiingen davon ab, wie stark sich die potentielle Energie I/ der Elektronen langs einer mittleren freien Weglange 1 iindert. Letztere ergibt sich aus der Beweglichkeitb gem30
.
A==-- m 4
.
b t.
8
Bei Zimmertemperatur folgt daraus mit
b,= 3600 cmaV-1sec-f , 1, = 2,s i O- s cm , t Siehe z.B. W.SHOCKLEY[la],
-
b,, = 4 700 cms V-1 set" [I1J : A,, = 1,2 10-5 cm . S. 277.
Reprinted Articles
438
HERBERT K R ~ M E: R
Fur Igrad Y )=eF
8 gibt
Beschrtinkungen auf Temperaturen
t GI. (lo) und ( 1 1 ) folgen aus GI. (3433) und (34,36) h i SOMMERWLD und B~~THJS [l7! mit C, C, und q,: ql = vl: vI. P
Reprinted Articles 111
440
HERBERT KR~ME :R
Damit wird
II,2b. Wenn GI. (8) erfullt ist, bewegt sich das Elektron bzw. Loch im Mittel durch das game Band hin und her, ehe es das niichste Ma1 stoflt. In den Impulsraum iibertragen heiBt dies, daB es sich glcich/iWzig quer durch die gesamte, zu diesem Band gehdrige BRrLLourN-Zone bewegt (Fig. 4 ) . Da die Quantenzustiinde im Impulsraum mit konstanter Dichte verteilt sind, h81t es sich in jedem Zustand gleich lange auf, und die StoBwahrscheinLichkeit ( I / T ) ergibt sich einfach als Mittelwert iiber die ganze BRILLOUIN-Zone. Unter Einfuhrung der freien Weglange 1 iind der Gruppengeschwindigkeit v =gradp E (P)heiBt das:
Fur die weitere Auswertung mtissen wir die schwerwiegende Annahme machen, daB 1 nicht nur am Bandrande, sondern auch im Bandinneren von der Geschwindigkeit und damit von P unabhtingig ist. Dann ist
Da uns die genaue Gestalt der Flgchen konstanter Energie im PRaum unbekqnnt ist, k6nnen wir diesen Mittelwert nicht exakt ausrechnen. Wir erhalten aber mindestens die richtige Gr6Benordnung, wenn wir den Gradienten in (16) durch die Grol3e
-&Fig. 4. Sehnitt cturrh den reduzlerten Impubraum rincs kiibischcn I>N this simplifies to
while for PfB the two Fermi levels penetrate into the allowed bands by the amount
*+
AB 1/2(pv - ZB) (1) and the injected carrier gas becomes d e generate. In the bias range =S
f r
+ A1 > qV >
CB
-I- 2Ar
(2)
the Fermi level penetration in the base re6 H. Krymer, T h e 0 of a Wide Gap Emitter for Transistorn. Paw. I R g vol. 45, UP. 1535-1537. Nov., 1957.
1783
gion exceeds that in the two injectors, In a homogeneous gap structure the potential barrier opposing the outBow of carriers from the middle region would have vanished at this point. But in the heterojunction structure the barrier still has the height O
p
€1
-I-AI - qV = d
+ Ar - (pV -
EB)
(3)
from the Fermi level in the base. So long as 0 > 0 a degenerately doped injector will be able to maintain the density in the base region against whatever outflow takes place into the opposite injector, which is the reason for the upper voltage limit in (2). The injected carrier density, then, exceeds the density in the injectors, a situation impossible to achieve with homogeneousgap junction structures. This is the situation shown in Fig. 1. At the upper end of the voltage range of (21, h = 6 / 2 , and this quantity can easily be a sizeable fraction of 1 ev, for example about 0.35 ev for the combination Ge-GaAs. Degenerate spill-over into the Ge central valley would occur already for AB ~ 0 . 1 4ev, which is considerably below 812. Structures with identically doped injector electrodes and an oppositely doped base are also possible and are probably easier to build. In this case the two injectors will have t o be a t the same potential, forward biased with respect to the base, The heterojunctions will again be efficient injectors of one carrier polarity, preventing the outflow of the neutralizing carriers of opposite polarity. There is no potential barrier for the injected carriers. But their outflow will still be substantially reduced because it would have to take place through the thin base, parallel to the junction. Even for conventional injection lasers the transverse junction dimensions commonly are at least of the order of a fraction of a millimeter. For such or even larger dimensions the resulting concentration gradients would be comparatively shallow, and because of this and because the base is likely to be thin compared to the transverse dimensions the outflow current would be low. Because of inevitable strong surface recombination one could not expect this low outflow if one of the junctions had been replaced by a surface. T he performance of lasers with identically doped injectors would, thus, fall in between that of conventional injection lasers, and tha t of oppositely doped hetercjunction lasers, being much superior to the former but not quite as good as the latter. For such injector materials like ZnSe and ZnTe that appear to be available only in one polarity only the identically doped version is possible. Because of the wider band gap of the injector the light from a heterojunction laser could be extracted through the injector, transverse to the plane of the junctions. This will not automatically be the case because the base thickness will often be much smaller than the lateral extension of the base and there will therefore be more gain in the parallel escape mode. However, if desired, this difference can obviously be overcome by a suitable device design. If this is done it is advisable to use fairly thin injector lay-
ers, in order to limit losses by freecarrier absorption in the injectors. In this way coherence over a much larger area could be obtained than in an ordinary injection laser. The predicted injection levels will occur only if radiationless recombination processes do not assume catastrophic magnitudes. The two main p r o c e m are volume losses via recombination centers in the base region, and recombination a t the heterojunctions proper. We have considered both processes, and have concluded that, in high-quality Ge a t least, recombination currents, say, in exc e s of lo00 A/cm-* could be caused only by the interface dislocations that arise from the lattice mismatch between base and injectors. For the Ge-GaAs system this mismatch is 0.7X10-'. Of the resulting dislocations all those will contribute to the recombination current that fall onto the lower-gap base side of the interface. The experimental values for the recombination efficiency of dislocation in Gevaryovera 1oOO:l range.7.8 If all the interface dislocations are assumed to contribute and if the most pessimistic values for the recombination efficiency' are chosen a rough calculation indicates recombination currents of the order 30,000 to 100,OOO 4/cm2, which would be sustainable only pulsed and which would very severely limit the practicality of the proposed device. Possibly the recombination efficiencies are lower than the most pessimistic values, but in any case these considerations teach the importance of a very close lattice fit and of retaining as many interface dislocations as possible on the high-gap injector side, where they would not contribute to the recombination current. The latter objective can be achieved by epitaxially growing the injector onto a pre-existing base a t a sufficiently low temperature, the first by a judicious selection of semiconductor materials and by improving the lattice fit by using alloy mixtures. For example, the already small misfit in the Ge-GaAs system can be made to vanish by alloying either the Ge with about 1.8 per cent Si or the GaAs with about 1.0 per cent GaSb or I d s . We have investigated the majority of the possible combinations containing Ge, Si, 111-V compounds and II-VI compounds. There are at least another two pairs with lattice misfits below (HgSe-ZnTe and InSb-CdTe) and a t least an additional 27 pairs with misfits below 10-2, even without alloying. Besides Ge-GaAs the most interesting combination appears to be Gap-AIP, which might provide a n indirect-gap visible laser. Perfect lattice fit could be obtained by alloying 4 per cent GaAs to the Gap. However, at present the Ge-GaAs system a p pears t o be the most immediately realizable one. HERBERTKROEMER Central Research Lab. Varian Associates Palo Alto, Calif. 7 G. K. Werthelm and G. L. Pearwn 'Recombination in Pkstically Deformed Gmnanium." Phvr. Fhv. vol. 107 pu 694-698 Auz 1957. ;A. D. K&. S. A. tulin."and B. L. Averback. .E5ects p' Growth Rate on Crystal Perfcctlon and Lifetime m Germadum.' J . A p p l . Phyr. vol. 27. UP. 1287-1290. Nov.. 1956.
Reprinted Articles 426
PROCEEDINGS OF THE IEEE
129 April
stimulated trap emptying studies. Present technology in this effort permits the fabrication of films with significantly higher mobilities and resistivities than those discussed in this communication. R. S. MULLES B. G. WATKINS Elec. Engrg. Dept. University of California Berkeley, Calif.
10 (.
r
s 0
.r a
P
Correction to "Relationships between Different Kinds of Network Parameters, Not Assuming Reciprocity or Equality of the Waveguide or Transmission Line Characteristics Impedances"'
I
3
2
5
4
103/TloKl
Fi
I Temperature de ndence of ballmobility pn for 8 s films.
TABLE I
5 6
8 9 10 11
32
0.13 0.06
6
24
4.4
10,ooo
-
0.07
270 1900 6.50
3.2 12 4
0.05 0.35 0.12
-
0.07 0.12 0.12 0.20 0.07 0.10
-
0.21 0.18 0.18 0.32 0.25 0.42 0.22
3 w c
-
880 820 750 760 730
I
23 23 100 200 200 140 160
Habake None None None None None None I
YdlW black 0-
yel-or.
Yd-W. 1
yd-or. yela.
D. M. KEARNS National Bureau of Standards Boulder, Colo.
-
I
'OO"q
The following has been called to the attention of the Editor. I n the relationship having the S-matrix on the left and expressions involving A , B , C,D,ZOIand 2 m on the right, a plus sign should appear in the denominator between the terms (B+CZaiZm) and (AZm+DZol). R. W.BEATTY
Manuscript r m i v e d February 11. 1964. 1 R W Bealty and D. M. Icarns €'Roc. IEEE
(~orrc&mxbcncc~. v o ~ 51. . p. 84; Januar;. 1%.
100
///
J -
07.C2d s films. The ordinate is normallzed at 4 W K .
Fi
Temperature dependenm of the reaislivitr
Considerations Regarding the Use of Semiconductor Heterojunctions for Laser Operation
p
of the reciprocal of the freesharge density, the sum of the activation energies for the mobility and the Hall coefficient should equal the activation energy of the resistivity, a s is observed.
DISCUSSION The observation of an exponential dependence for Hall mobility on temperature in deposited CdS films was first reported by Berger.' Such a dependence has also been found in deposited films of PbS, and, following the analysis of Petritz.' it is often ascribed I H. Berger 'obcr das Ausheilen von Cittcrfehk n friachaufgkampfter CdSSchIchten (I)." Plrrr. Slatus Sdidi. vol. 1, UP. 739-751, July 1961 4 R. L. Peuitz 'Theory of bhotdcond;ctivity in amiconductor til&" Phrs. Rm..vol. 104, PP. 150815~6; D s t m b u . 1956.
f
P I
Flp. 3-Tempraturr dependence of the Hall constant Rn for deposited CdS films. The ordinate is normalized at 400°K.
t o scattering a t the boundaries between the small crystallites which make up the film. There is reason to doubt this hypothesis chiefly because of the near independence of the observed Hall-mobility value on crystallite size. This view is corroborated by Berger.' IVork is now going on in this laboratory to ascertain whether or not the observed mobility dependence is not resultant from the large deeptrap densities that are known to characterize these films. This information is being sought through photo-Hall effect measurements, and through thermally-
In a recent communication,' Kroemer has proposed a new injection scheme using heterojunction: for possible laser action, in which a n indirect-gap semiconductor, say Ge. is sandwiched between two direct-gap semiconductors of opposite types, say nand p-type GaAs. In our laboratory, we also have considered the feasibility of using heterojunctions for laser work based on a different scheme. Kroemer's proposal presupposes that 1) injected electrons and holes would be trapped in the center region by potential barriers a t the two heterojunctions and 2 ) laser action would eventually occur a t sufficiently high carrier injection levels. The argument presented in his communication. however, is rather vague and misleading. Lye would like to discuss theoretical considerations in using heterojunctions for laser operation and to present our scheme in view of these considerations. Manusriot received lanuarv 31. 1964. The TC?earchr&ried herein is made h b l c through mup
wrt rmivcd from the Departments d Army, Naw and Air F o r e under mant AF-AFOSR-139-63. I H. Kroemer", 'A Propoeed class of heterojunction injection lasers. Pam. IEEE (Canupondenu). vol. 51. up. 1782-1783; December. 1963.
130 Selected Works of Professor Herbert Kroemer 1964 The focal point is the lifetime of excess carriers in a radiative recombination process. For degenerate direct-gap semiconductors, the lifetime, given by the reciprocal of Einstein’s coefficient of spontaneous emission, is of the order lo-” sec. In indirect-gap semiconductors, however, the radiative recombination process must be accompanied by phonon or impurity scattering t o conserve momentum and, consequently, the lifetime of such a process is much much longer. This is manifested by the fact that the quantum efficiency of recombination radiation in GaAs diodes is close to unity while that in Ge diodes is less than lo-’. I t is to be recognized that energy pumped into a diode is ultimately converted into lattice heat if not into coherent radiation. Therefore, the second assumption made by Kroemer not only needs theoretical scrutiny but may become academic in practical reality. Two principal schemes [l], [Z] have been proposed to achieve laser action in indirectgap semiconductors: first, to tunnel electrons into the (OOO) valley and second, to get an admixture of the various conduction band minima and the (@XI)valley states through proper impurity states. The scheme t o be presented here falls into the first category. Consider an n-n heterojunction of Ge-GaAs with its energy band diagram shown in Fig. I(a).
42 I
Correspondence supply exholes and electrons with k(000) for radiative recombination in the center region. Degeneracy in outer regions is necessary for heavy injection to shorten the lifetime of excess carrier so that the radiative recombination process may compete favorably with scattering processes. A detailed discussion may be found in [I]. I t should be pointed out that even in the scheme proposed by Kroemer. excess carriers can not pile up indefinitely in the center region. After a quasi-equilibrium state is reached, the flow of electrons and holes from one outer region to the other can be described directly by quasi-Fermi levels without reference to the center region if recombination in the center region is neglected. That means, the flow of current is governed by the law of diffusion of excess minority carriers in GaAs and the situation is no better or no worse than that in a homogeneous diode. The statement made by Kroemer is misleading because it implies that great benefit can be derived from pctential barriers a t heterojunctions. In summary, we believe that the function of heterojunctions in laser work is to supply the right kind of electrons with k(000) to an indirect semiconductor. In view of Anderson’s work, the n-n heterojunction seems suitable for such a purpose. The question still remains, however, as to how long electrons will stay in the (OOO) valley. Therefore, phonon and impurity scattering should be minimized to enhance the probability of radiative recombination. S. WAXG C. C. TSENG Dept. of Elec. Engrg. University of California Berkeley, Calif.
valley in germanium is just over loyocm-8. This admittedly is a high number but an extension of the Hall-Shockley-Read recombination theory into the degenerate range indiates that the nonradiative recombination a t this level would not be prohibitive. provided this injection level can be obtained in the first place. The latter is the function of the heterojunction injectors. 2) I have never claimed that charge carriers can pile up indefinitely in the base region, but merely that degenerate injection levels can be obtained that are much higher than with a homojunction structure, and high enough to cause degenerate spill-over into the central valley of Ge. \Tang and Tseng state correctly that “the flow of elecif recombination in the center trons. is governed by the region is neglected law of diffusion of exces minority carriers in GaAs” but they do not show why this fact should contradict rather than support my statement and why the situation should be ”no better or no worse than that in a homogeneous diode.” I n the absence of a justification for their claim, I must maintain that indeed “great benefit can be drived from potential barriers a t heterojunction” and must refer for the proof to my previous correspondence and to my 1957 paper quoted therein. HERBERT KROEMER Central Research Lab. Varian Associates Palo Alto, Calif.
..
...
REFERESCES
lascr structure under a forxard bias conditidn.
The nature of current flow across the junction has been analyzed in detail by Anderson [3]. For electrons going from Ge to GaAs or vice versa (a combination of electron emission and tunneling), both the momentum and energy of the electron are conserved. That means, if GaAs is negatively biased with respect t o Ge, electrons from GaAs will go to the (OOO) valley of the conduction band of Ge as in direct tunneling. To prevent the (OOO) valley electrons from being scattered into the conduction band minima, the device must be operated a t low temperatures and the doping concentration of Ge must be low. No mention is made in Krwmer’s paper about scattering processes; apparently he is concerned with the indirect transition while we are interested in the direct transition in Ge. The present heterojunction scheme of getting (OOO) valley electrons may be superior to the tunnel scheme proposed earlier 11) because high doping concentration in the indirect-gap semiconductor is not required here. The proposed laser structure is shown schematically in Fig. l(b), which consists of, from left to right, regions of degenerate p t y p e Ge, near intrinsic, n-type Ge and degenerate n-type GaAs. The Ge p-n junction and the Ge-GaAs n-n junction are t o
S. Wang “Proposalfor a two stage s m i p d u c t o r laser &ugh tunneling and injection 1. Appl. Phys., vol. 34. PP 3443-3450; Dmmder, 196.3. P. &grain private communcation. R. L. h d u s o p , ‘Expriments w Ge-GaAs heterojunctions ScJid-SWm &cboricr, vol. 5 PD. 341-351; P~rgamonPrewr, New York, N. Y.: 4 u.) I41 ‘Germanium-Gallium Aracnlde Contacts * P h . 6 . disartation. lkpartment of Electrich EnginevLng. S m c u s University, N. Y.; 1059.
Author’s Reply2 I wish to comment only on those parts of the above communication that seem to contain a criticism of my proposal, not upon Wang and Tseng’s proposal that is intimately intertwined with this criticism. 1) I stated in my paper that in indirect gap semiconductors laser action “could take place by spill-over of electrons from their lowest energy valleys into the region of the smallest direct gap.” Obviously, then, I was referring to direct transition, under conditions where the electrons in the central valley are essentially in equilibrium with those in the outlying valleys. I n such a case it is irrelevant how short the interband relaxation time in the central valley is, and into which valley the electrons are originally injected. In fact, if the original injection should take place into the lower outlying valleys, a short interband relaxation time might be desirable. The total injection level necessary t o reach degeneracy in the central
WWV and WWVR Standard Frequency and Time Transmissions The frequencies of the National Bureau of Standards radio stations W V V and W W H are kept in agreement with respect to each other and have been maintained as constant as possible since December 1, 1957 with respect to an improved United States Frequency Standard (USFS).’The corrections reported here were arrived a t by means of improved measurement methods based on transmissions from the NBS stations WWTB (60 kc) and U’WVL (20 kc). The values given in the table are 5-day running averages of the daily 24-h our values for the period ending a t 1800 UT of each day listed. The time signals of WIW and WWVH are also kept in agreement with each other. Since these signals are locked to the frequency of the transmissions, a continuous departure from UT2 may occur. Corrections are determined and published by the U.S. Naval Observatory. The time signals are maintained in close agreement with UT2 by properly offsetting the broadcast frequency from the USFS a t the beginning of each year when necessary. This new system was commenced on January 1, 1960. Manuscript rmived Febru 24. I N . See ‘National Sendardsytime and frequency
’
:Manuscript received February 14. 1964.
in the United States. Pnoc. IRE (Conrrbond8nrr). vol. 43, pp. 105-106; January, 1960.
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If, in discussing a problem in semiconductor device physics, you cannot draw an energy band diagram, then you don't know what you're talking about. ' '
Herbert Kroemer
Reprinted from
H. Kroemer, .'Meterostructures for Everything: Device Principle of the 1980's?", Japan. J. Appl. Phys., Vol. 20 (Suppl. l), pp. 9-13,1981. Copyright 1981, with permission from IPAP.
132 Selected Works of Professor Herbert Kroemer proceedings of the 12th conference on Solid State Devices, Tokyo, 1980; Japanese Journal of Applied Physics, Volume 20 (1981) Supplement 243-1, pp. 9-13
(Invited) Heterostructures for Everything: Device Principle of the 1980’s? Herbert KROEMER Department of Electrical and Computer Engineering, University of California, Santa Barbara, California 93106, USA
One of the dominant themes of semiconductor device R & D during the 1980’s will be the incorporation of heterostructures into most existing kinds of devices, and the emergence of new kinds of devices made possible by heterostructures. In this paper the power of heterostructures as a design tool is illustrated by discussing several ways in which the incorporation of heterostructures Can improve the bipolar transistor. The dominant idea is that energy gap variations are a powerful way to control carrier flow; in bipolar structures they permit the control of electrons and holes independently. Several applications of this principle are discussed, going beyond the familiar wide-gap emitter concept, and including several concepts not previously discussed in the literature. The paper closes with a brief discussion of non-bipolar applications and speculative future applications.
examples of non-bipolar applications will be given in the last part of the paper.
$1. Introduction It has now been ten years since the experimental realization of the double heterostructure laser. Such lasers are today used in actual communications systems, and the heterostructure technology is rapidly spreading to other devices. I believe that one of the dominant themes of semiconductor device R & D during the 1980’s will be the incorporation of heterostructures (HS’s) into every kind of semiconductor device whose performance can be improved by such an incorporation, and for which the improvement is sufficiently desirable to justify the technology. Such improvements can be made in almost all classes of devices. Finally, new kinds of devices made possible by HS’s are rapidly emerging, and will assume an increasing role toward the end of this decade. Rather than attempting to cover every conceivable application of HS’s, I shall try to illustrate the power of HS’s as a design principle by concentrating on the variety of ways how their incorporation can drastically improve the familiar bipolar transistor. The underlying idea is that energy gap variations are a powerful way to control carrier flow, in addition to the control exerted by the electrostaticpotentials generated by doping and bias. In bipolar structures, energy gap variations can be used to control electron and hole flows separately. Various
52. Heterojunction Bipolar Transistors
2.1 Wide-gap emitters The idea that the performance of a bipolar transistor could be improved by increasing the energy gap in the emitter relative to the base is as old as the bipolar transistor itself.‘) Consider an npn transistor with an energy band diagram as shown in Fig. 1. The operating principle of the device is the injection of electrons from the emitter into the base, and their subsequent collection by the collector. Asso-
FERMI LEVEL
VC
I Fig. 1. Energy band diagram and carrier flow in an npn transistor with a wide-gap emitter. The heavy broken line in the emitter shows the valence band edge as it would exist in a homojunction transistor with the same emitter doping.
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ciated with the desired emitter-to-base electron 1O00, much larger than the B-values of even the injection is an undesirable base-to-emitter hole best conventional transistors.* Some of these injection. This hole injection current is part of results were on phototransistors, which are the base current; at high current levels it is easier to construct than true three-terminal often the dominant part. In order to have a devices. desirable current gain fi=I,/Z, of about 100, The high-frequency performance still lags the hole injection current from base to emitter appreciably behind that of Si transistors, and must be kept below 1% of the emitter-to-base even more behind the theoretical possibilities, electron injection current. In conventional largely due to non-optimized technologies. For transistors this is achieved by a high emitter-to- true three-terminal devices, only three pabase doping ratio of typically about 100: 1. This pers1°-12) have so far reported performance is the dominant design constraint in conven- above 100 MHz, up to ftr1 GHz. The fastest tional bipolar transistors. HS transistors so far are phototransisSuppose now that the emitter band gap is tors.8.’3.’4) In one case,I3) response times as increased beyond that of the base. If the emitter short as 1 nsec have been reported. Considering doping is (initially) kept unchanged, all the in- the high gain of these devices (>>loo), this crease in energy gap goes into depressing the would correspond to sinusoidal operating frevalence band edge, introducing an additional quencies up to many gigahertz. Perhaps more energy bairier into the path of the hole flow, but significant: This particular device is the first not into the path of the electron flow. The re- high-performance bipolar transistor reported sult is a reduction of the base-to-emitter hole in the literature that was prepared by MOCVD injection current by a factor exp (- Aa,/kT). rather than LPE. With the rapid progress in This is incredibly effective: Energy gap differ- MOCVD and MBE, one may expect the future ence of several tenths of 1 eV are readily avail- progress in transistor frequency performance able, and their effect is so large that the base- to be rapid. The technology of HS transistors is likely to to-emitter hole injection current becomes negligible, regardless of the emitter-to-base be dominated by III/V compounds, because of doping ratio. The current gain p will be limited the comparative ease with which the new only by the recombination currents. It was epitaxial technologies permit the preparation of recognized by Kroemer” that this could be defect-free HS’s in lattice-matched IIIjV cqmutilized to improve the transistor by using a pound pairs. Promising lattice-matched III/V much higher base doping and a much lower systems in addition to (Al, Ga)As-on-GaAs are emitter doping. One result would be a greatly (Ga, 1n)P-on-GaAs and InP-on-(Ga, In)As.I4) Because of the extremely high state of dereduced p-falloff with current than in conventional transistors. If the emitter doping were velopment of Si-1C technology, there is a reduced below the value that the base doping strong incentive to develop an HS-IC techhas in a conventional transistor (‘‘super- nology for Si, even if its ultimate performance inverted” doping), the emitter capacitance is less than for an all-III/V compound techwould be reduced, with benefits for the high- nology. Very promising results in this direction frequency performance. It was subsequently have been obtained by Matsushita et al.”) who recognized3-’) that an even greater improve- used an emitter made from amorphous SO,, ment in frequency response would result from which has a wider energy gap than Si. It rethe reduction in base resistance that could be mains to be seen what the high-frequency potenobtained by a drastic increase in base doping. tial of this combination is; the low-frequency Maximum oscillation frequencies fmax of current gain (pa500) is excellent. 100 GHz and more have been p r e d i ~ t e d . ~ ~ ~ .A ~ ’potentially very promising system is GaPAs a result of rapid progress in the hetero- on-Si. The two semiconductors are fairly well epitaxial growth of III/V compound semi- lattice-matched (within 0.4 %); however, good conductors, especially GaAsf(Al,Ga)As, it *This field lacks a good recent review. References 7-14 appears that these predicted improvements are give only recent results for which /9>1000 or f> about to become realized in practice. Several 100MHz. For references to most of the earlier have reported p-values over pioneering papers see ref. 5.
134 Selected Works of Professor Herbert Kroemer 11
Heterostructures for Everything ?
epitaxy of GaP on Si appears to be hard to achieve. The first Gap-on-Si transistor, prepared by VPE, has been reported by Katoda and Kishi,I6) with (so far) very low j?-values. In our own laboratory, we are attempting to grow GaP emitters on Si by MBE. A detailed theoretical estimate6) suggests that npn GaponSi transistors with a maximum oscillation frequency f,,, up to about 100 GHz should be achievable. It remains to be seen what will come of these Gap-on-Si efforts.
2.2 Wide-gap collectors In most bipolar logic families (ECL is the dominant exception) the collector is fonvardbiased during part of the logic cycle. If the base is more heavily doped than the collector, this causes major base-to-collector injection of holes, which increases dissipation and slows down the switching speed. Using a wider energy gap on the collector as well as on the emitter side, suppresses this highly undersirable effect.6) In IzL, this is not a problem, but 12L has problems of its own, which also suggest HS’s as a solution; see below.
BASE
/I
i3
EMITTER
i
CCCLECTOR
Ii:
f
Fig. 2. Two-base layer design in a heterojunction transistor. The external base layer has, on top of a thin narrow-gap layer, a thick very heavily doped second base layer extending right to the emitter junction, minimizing the external base resistance. Because of the wider energy gap, negligible currents will flow through this part of the emitter junction.
sides, this part will have its current density reduced by the same Boltzmann factor by which the base-to-emitter hole injection is depressed. Using a different terminology: the vertical part of the junction is biased below its turn-on voltage, which is higher than that of the horizontal part by approximately A&,/q. Because the emitter would be weakly doped, the effect of a deep sidewall on the emitter capacitance is small, and emitter-base tunneling cannot occur 2.3 Utilizing turn-on voltage diflerences at all. Yet the high conductivity of the upper base layer in effect brings the base contact as 2.3.1 Double base layers We may view the role of HS’s as providing close to the emitter-base junction as is physibarriers to control the flow of electrons and cally possible. In fact, this design has been holes independently of each other. The idea of used in the HS transistor reported in ref, 11. the wide-gap emitter and collector was to block 2.3.2 Wide-gap sidewalls and injection barriers the flow of holes (in an npn transistor, electrons The idea to use energy gap variations to in a pnp). The idea can be extended to control suppress carrier injection into portions of the the flow of the carriers with opposite polarity base region where no injection is desired, is an as well. Ladd and Feucht3) pointed out that it important new concept, the power of which is desirable, in an HS transistor just as in a does not appear to have been widely recognized. conventional transistor, to have a thick base The lateral pnp transistor in 12L is an example region outside the emitter, and that the realiza- of a device that could be greatly improved by tion of the full promise of the HS transistor incorporating this idea. In homostructure might well hinge on achieving a suitable device designs, this transistor is always a poor transisgeometry. It was pointed out by this writer6) tor. It could be greatly improved by an HS that a natural solution to this problem lies in geometry as, for example, in Fig. 3. The actual a thick planar design in which the outer base transistor is the all-narrow-gap p’np structure consists of two layers, the upper one of which shown embedded between the two wide-gap has the same wide energy gap as the emitter layers. The two wide-gap p‘np transistors and is very heavily doped (Fig. 2). In a homo- above and below it are biased below turn-on; structure transistor, such a design would lead their n-type base regions simply act as walls to to a disastrous loss of fl, emitter-base tunneling confine the injected holes in the true n-base. effects and a high emitter capacitance. In an HS Because of the small hole diffusion lengths in transistor, because the vertical part of the III/V compounds, the implementation of such
emitter junction has a wide energy gap on both
a structure will require submicron technologies.
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T‘
GAPS:
-__
___
NARROW
WIDE
__ __
---
-----
N
P+
P
---
Fig. 3. Injection current in a lateral pnp transistor, as in 12L. Only the narrow-gap portion (n) of the base carries current. BASE
\
Fig. 5 . Energy bands in a modulation-doped multilayer structure. All donors are contained in the wide-gap layers, all electrons in the narrow-gap layers.
COLLECTORS
I EMITTER
Fig. 4. Supression of electron injection into selected portions of the base region in I’L, by means of wide-gap injection barriers, achieved by pulling the emitter-base junction into the wide-gap region of the structure.
Another example of suppression of undesired injection is the following. In IZL, a significant fraction of the base area is in contact with the emitter, but not with one of the collectors. Electron injection into those portions of the base creates stored charge that wastes power and slows down the switching speed. In an HS-IZL design, this could be avoided by simply pulling the emitter-base pn junction below the hetero-interface, into the wide-gap region, as shown in Fig. 4.
53. Beyond Bipolar Transistors The detailed discussion of the bipolar transistor was intended as an example. There probably does not exist a kind of device that cannot be similarly improved by the incorporation of HS’s. Space does not permit me to say more than a few words about these other possibilities. Perhaps the most powerful general design principle applicable to many non-bipolar devices involves the use of thin (oriented interfaces, and in fact for all interface orientations except those in which the interface is parallel to one of the (1 11) bond direction. The condition for this can be expressed as a mathematical condition on the Miller indices ( h k l ) of the interface [54]. Let [ hkl] be the direction perpendicular to the interface plane. The plane is parallel to one of the (1 11) bond
-
11103
Fig. 12. Atomic arrangement and electrostaticpotential at an ideal Ga/GaAs(llO) interface. Each GaAs plane parallel to the interface contains an equal number of Ga and As atoms and is hence electrically neutral. From ref. [S I I.
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/ Heterostructure
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Ga P
Si
Fig. 13. Atomic arrangement at idealized GaP/Si(ZI 1) interface, from ref. [54]. As in the (1 10) case, each G a P plane parallel to the interface contains an equal number of Ga and P atoms and is hence electrically neutral. But in addition, the bonding of the “black” sublattice sites across the interface is much stronger (two bonds) than that of the ”white” sublattice sites (one bond). When G a P is grown on Si, this bonding difference can be utilized to achieve growth free of antiphase disorder, with the “black” sublattice occupied by P atoms, the white by G a atoms.
directions if [ hkl] is perpendicular to that direction. This implies [hkl] * (111) = + h
* k & I = 0,
for at least two of the eight possible independent sign combinations. The simplest such orientation is the (1 10) orientation, already recognized as such and intensively discussed by HKWG. The next-simplest orientation is (1 12>, followed by (123), etc. Figs. 12 and 13 show the atomic arrangements at a (1 10) and at a (1 12)-oriented polar/nonpolar interface, both viewed again in the [ilO]direction. In the absence of specific reasons to do otherwise, it is probably advisable to use the lowest-index orientation for the epitaxial growth. If only the nonpolaron-polar growth sequence is needed for a particular device, the (110) orientation may indeed be the preferred orientation. Inasmuch as the (1 10) planes are the natural cleavage planes of III/V compounds, this happily coincides with the natural interest of the surface physicist in this orientation: Most of the non-device studies of the initial growth of Ge on GaAs have indeed used these planes. However, if the polar-on-nonpolar growth sequence is demanded (which automatically induces polar/nonpolar superlattices), altogether new considerations intervene.
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5.3. Polar-on-nonpolar growth: the site allocation problem
When, in a polar/nonpolar heterosystem, the polar (compound) semiconductor is to be grown on the nonpolar (elemental) one, a new problem arises [54,55]: Avoiding antiphase disorder in the growing compound semiconductor. This problem does not exist at all in element-on-compound growth, and it is at most a minor problem in compound-on-compound growth. But for compound-on-element growth it is as severe and fundamental as the interface neutrality problem at (00I} polar/nonpolar interfaces, and it totally dominates the problem of polar-on-nonpolar growth for nonpolar orientations, such as (110) and (112). When a binary compound with two different atoms per primitive cell (e.g. GaAs, Gap) is grown on an elementary substrate (e.g. Ge, Si) in which the two atoms are identical, there exists an inherent ambiguity in the nucleation of the compound, with two different possible atomic arrangements, distinguished by an interchange of the two sublattices of the compound. If different portions of the growth exhibit different sublattice ordering, antiphase domains result, separated by antiphase domain boundaries, a defect similar to grain and twin boundaries. For high-performance devices, antiphase domain boundaries must almost certainly be avoided, which calls for a rigorous suppression of one of
a
GO -LIKE-,
r A ~ - ~ ~ ~ E
b Fig. 14, (a) Occurrence of antiphase domain disorder in the growth of GaAs on an unreconstructed Ge (1 10) surface, due to the absence of a built-in bonding difference for the as-yet unoccupied surface sites belonging to the two sublattices. (b) Creation of Ga-like and As-like electronic configurations in the top Ge (1 10) atomic layer, due to reconstruction,aiding in the suppression of antiphase disorder inside the GaAs. From ref. [SS].
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the two nucleation modes. The problems in doing so depend very strongly on the exact atomic arrangement and on the dangling-bond configuration at the surface of the elemental semiconductor substrate. Unfortunately, they are particularly severe for the simplest nonpolar interface orientation, the { 1 lo} orientation. The situation is illustrated in fig. 14a, which shows that on an ideal and perfectly flat ( = unreconstructed) Ge (1 lo} surface the sites subsequently to be occupied by G a and by As atoms have no built-in distinction between themselves. The relative Ga/As ordering at different nucleation sites should therefore be perfectly random, which in turn would lead to a high degree of antiphase domain disorder, with domain sizes of the order of the nucleation site separation, which is usually very small for good epitaxial growth. The situation on the { 112) surface is far more favorable. As fig. 13 shows, the unoccupied sites ahead of an ideal (1 12) surface are of two quite different kinds: Sites (labelled 1 in fig. 13) with two back bonds to the Si surface, and sites (Nos. 2 and 4) with only one back bond. One easily sees that the two kinds of sites belong to the two different sublattices. Now it is well known that the column-V elements P, As, and Sb, form chemical compounds with Ge and Si, whereas the column-111 elements Al, Ga and In do not. One might therefore expect that the strongly-bonding column-V atoms might displace any columnI11 atoms from the doubly back-bonded sites (No. 1). But once site No. 1 has been occupied by a column-V atoms, site No. 2 becomes more favorable for occupancy by a column-I11 atom than by a column-V atom. This, in turn. favors occupancy of site No. 3 by another P atom, followed by another Ga atom on site No. 4. Apparently, this is indeed that happens: We have grown GaP on Si (112) by MBE [54], and tests show that the observed sublattice ordering is as described here, with no evidence of antiphase domains. Furthermore, although the electrical properties of these first Gap-on-Si { 112) interfaces are still far from ideal, we were able to build bipolar n-p-n transistors with an n-type GaP emitter on a Si p-n base/collector structure, with emitter injection efficiencies up to 90%. This is still far below what would be desirable for practically useful devices ( > 99%),but is far better than anything else ever achieved in the very difficult Gap-on-Si system. It raises the hope that device-quality polar-on-nonpolar hetero-interfaces might in fact be achievable. Our above theoretical speculation was oversimplified in that the reconstruction of the free Ge or Si surface, which is unquestionably present, was ignored. because of the strong bonding difference present already in the unreconstructed {I 12} surface, any reconstruction on that surface [56]should be little more than a quantiative complication, unless the reconstruction somehow destroys the strong inherent surface site inequivalence, which is extremely unlikely. The situation on the (110) surface is entirely different. Here any reconstruction would creure a site inequivalence (see fig. 14b), and if this inequivalence is of the right kind, it might convert a hopeless orientation into a promising one. As we have pointed out elsewhere [55]. the simplest possible
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reconstruction, a bond rotation similar to that on GaAs {OOl}, and postulated by Harrison (571 to occur on Si {I lo}, is exactly of the most desirable kind. In fact, growth of GaAs on Ge (1 lo} apparently free from antiphase disorder can be achieved under certain growth conditions [55], which unfortunately however do not appear to lead to device-quality electrical properties. The (1 12) surface, which has a built-in strong site inequivalence, is therefore preferable over the reconstructed { 1lo} surface, which must rely on a tenuous surface reconstruction to achieve site selection. Our experimental experience [54] strongly confirms this expectation. We therefore consider our own former advocacy [55] of the reconstructed {I lo} surface as having been superseded by the subsequent realization of the inherently greater promise of the (1 12) orientation. 5.4. Small misorientations: nuisance or design parameter? There is no such thing as a perfectly-orientedcrystallographic interface. Any real interface will have deviations from perfect flatness and perfect orientation, as a result of which the (1 1 1) bonds are rotated out of the true hetero-interface plane by a small but non-zero angle 8. At apolar/nonpolar interface this will cause a finite built-in interface charge to appear, and even for small misorientations the resulting charge may be large by device standards. For the { I 12) interface, the charge density is easily shown to be u = (& / a 2 )
sin 8 .
If the tilt angle is small enough, this charge is not likely to be removed by the HKWG atomic re-arrangement, but is likely to act as a permanent tilt doping. A wafer orientation to within f 0.5” ( s 10 milliradian) is roughly the practical limit of current routine wafer orientation techniques. Assuming the lattice constant of GaAs, such a misorientation corresponds to an interface charge density of 4.7 X lo’* elementary charges per cm2. This is a large charge, and much more accurate wafer orientation techniques than are in current use will be necessary. This is of course possible, but is a major nuisance. A highly (1 12)-selective etch would certainly help. However, one man’s nuisance is often the next man’s design parameter. If the orientation could be controlled to significantly better than radian, a deliberate misorientation might become a practical means of introducing desirable interface charges into devices such as HEMT’s. Because the interface charges would not be randomly distributed, but be located on quasiperiodic interface steps, they would scatter less, and even new superlattice effects might arise. Finally, by deliberately creating a controlled local variation in the interface tilt, one might even introduce lateral “doping” variations into device structures. It is a fitting notion on which to close a paper that addresses itself to the role of interfaces in submicron structures, more specifically, to the role of the interface nanostructure in determining the properties of devices containing those interfaces.
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Acknowledgments It is a pleasure to thank Dr. R.S.Bauer for inviting me to present this paper at this Symposium, and thereby providing the stimulus to order my thoughts on the topics discussed and to put them down on paper, something that otherwise would have been unlikely to occur. Many thanks are due to Drs. E.A. Kraut, J.R. Waldrop, R.W. Grant, D.L. Miller and S.P. Kowalczyk. for uncounted discussions. Last, but not least, I wish to acknowledge the profound influence that Professor W.A. Harrison has had on my thinking.
References [ I ] See, for example, H. Kroemer, Japan. J. Appl. Phys. 20, Suppl. 20-1 (1981) 39. [2] H. Kroemer, Proc. IEEE 70 (1982) 13. [3] W. Shockley, US Patent 2,569.347, issued 25 Sept. 1951. [4] R.L. Anderson, Solid-state Electron. 5 (1962) 341. [5] For a general review. see A.G. Milnes and D.L. Feucht. Heterojunctions and Metal-Semiconductor Junctions (Academic Press, New York. 1972). (61 An excellent recent review is contained in chs. 4 and 5 of H.C. Casey and M.B.Panish, Heterostructure Lasers (Academic Press, New York, 1978). [7] H. Kroemer, Proc. IEEE 51 (1963) 1782. [8] R. Dingle, in: Festk6rperprobleme/Advances in Solid State Physics, Vol. 15, Ed. H.J. Queisser (Vieweg, Braunschweig. 1975) p. 2 1. [9] R. Dingle, H.L. Starmer, A.C. Gossard and W. Wiegrnann. Appl. Phys. Letters 33 (1978) 665. [ 101 For a recent review, see T. Mimura. Surface Sci. 113 (1982) 454. [ l l ] For a review, see N. Holonyak, R.M. Kolbas. R.D. Dupuis. and D.D. Dapkus, IEEE J. Quantum Electron. 16 (1980) 170. [I21 H. Sakaki, L.1. Chang. R. Ludeke, C.-A. Chang, G.A. Sai-Halasz and L. Esaki. Appl. Phys. Letters 31 (1977) 21 1; see also L.L. Chang and L. Esaki, Surface Sci. 98 ( 1 980) 70. [13] H. Kroemer, W.-Y. Chien, H.C.Casey and A.Y. Cho, Appl. Phys. Letters 33 (1978) 749. [I41 H. Kroemer, W.-Y. Chien, J.S. Hams, Jr. and D.D. Edwall, Appl. Phys. Letters 36 (1980) 295. [ 151 Y.Z.Liu, R.J. Anderson, R.A. Milano and M.J. Cohen. Appl. Phys. Letters 40 (1982) 967. [I61 See, for example, J.R. Waldrop. S.P.Kowalczyk, R.W. Grant, E.A. Kraut and D.L. Miller. J. Vacuum Sci. Technol. 19 (1981) 573. [I71 G.F. Williams, F. Capasso and W.T. Tsang, IEEE Electron Devices Letters 3 (1982) 71: see also F. Capasso, Surface Sci. 132 (1983) 527. [I81 H. Kroemer, Critical Rev. Solid State Sci. 5 (1975) 555. [ 191 W.A. Hamson, J. Vacuum Sci. Technol. 14 (1977) 1016; see also ref. [24] below. [20] G. Margaritondo, A.D. Katnani, N.G. Stoffel, R.R. Daniel and T.-X. Zhao, Solid State Commun. 43 (1982) 163; see also G.Margaritondo, Surface Sci. 132 (1983) 469. [21] J.L. Shay, S. Wagner and J.C. Phillips, Appl. Phys. Letters 28 (1976) 31. [22) J.C. Phillips, J. Vacuum Sci. Technol. 19 (1981) 545. [23] W.R. Frensley and H. Kroemer, Phys. Rev. B16 (1977) 2642. [24] W.A. Harrison, Electronic Structure and the Properties of Solids: The Physics of the Chemical Bond (Freeman, San Francisco, 1980): see especially section 10F.
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[25) J.O. McCaldin, T.C. McGill and C.A. Mead, Phys. Rev. Letters 36 (1976) 56. These authors
expressed the correlation between valence band lineup and anion electronegativity for Schottky bamers; the approximate applicability of their result to heterojunctions appears to have been discussed first by W.R. Frensley and H. Kroemer, J. Vacuum Sci. Technol. 13 (1976) 810; see also ref. [23]. [26] For a very “physical” discussion of this theoretical foundation, see Harrison, ref. [24]. especially chs. 1-3 and ch. 6. [27] S.J. Anderson, F. Scholl and J.S. Harris, in: Proc. 6th Intern. Symp. on GaAs and Related Compounds, Edinburgh, 1976, Inst. Phys. Conf. Ser. 33b (Inst. Phys., London and Bristol, 1977) p. 346. [28] The numerical values are based on Harrison’s table 10-1 on p. 253 of ref. [24], except that we use the values from ref. 1271 for the energy gaps of GaSb and AlSb. [29) J.A. Van Vechten. Phys. Rev. 87 (1969) 1007. Van Vechten gives an extensive table of theoretical ionization energies, from which electron affinities are easily obtained by subtracting the energy gaps. [30] This broken-gap lineup is, in fact, predicted by all three major predictive theories: The electron affinity rule, the Frensley-Kroemer theory, and the Harrison theory. [31] G.C. Osbourn, J. Appl. Phys. Letters 53 (1982) 1536: J. Vacuum Sci. Technol. 21 (1982) 469: see also ref. [34] below. [32] G.H. DBhler, Phys. Status Solidi (b) 52 (1972) 79,553; G.H. Ddhler, H. Kiinzel and K. Ploog, Phys. Rev. B25 (1982) 2365. [33] Our calculation is to illustrate the basic idea only. The quoted composition Falls into a solid solubility gap of uncertain width the existence of which has been reported. It may therefore be difficult or impossible to prepare. For a discussion and further references on this point see ch. 5 of ref. [6]. [34] P.L. Gourley and R.M. Biefeld, J. Vacuum Sci. Technol. 21 (1982) 473; G.C. Osbourn, R.M. Biefeld and P.L. Gburley. Appl. Phys. Letters 41 (1982) 172. [35] M.E. Davis, G. Zeidenbergs and R.L. Anderson, Phys. Status Solidi 34 (1969) 385. [36] G.M. Guichar, C.A. SCbenne and C.D. Thuault, Surface Sci. 86 (1979) 789. 137) R.S. Bauer and H.W. Sang, Jr., Surface Sci. 132 (1983) 479. (381 H. Morkoc, L.C. Witkowski, T.J. Drummond, C.M. Stanchak. A.Y. Cho and J.E. Greene. Electron. Letters 17 (1981) 126; see also H.L. Stdrmer. Surface Sci. 132 (1983) 519. (391 It has been suggested by W.I.Wang (personal communication) that the (110) sequence dependence might be related to an as yet unexplained instability of (1 IOForiented (Al, Ga)As growth observed by him.For another report of a different kind of (1 lo} growth instability see P. Petroff, A.Y. Cho. F.K.Reinhart, A.C. Gossard and W. Wiegmann, Phys. Rev. Letters 48 (1982) 190. [40]R.C. Miller. W.T.Tsang and 0. Munteanu, Appl. Phys. Letters 41 (1982) 374. [41] E.A. Kraut, R.W. Grant, J.R. Waldrop and S.P. Kowalczyk, Phys. Rev. Letters 44 (1980) 1620. [42) H.Kroemer and W.-Y. Chien, Solid-state Electron. 24 (1981) 655. [43] H.K. Gummel and D.L. Scharfetter, J. Appl. Phys. 38 (1967) 2148; see also C. Kittel and H. Kroemer, Thermal Physics, 2nd ed. (Freeman, San Francisco, 1980) ch. 13. For very unsymmetrically doped junctions. the G S correction is between 1 kT/q and 2 kT/q. I441 H. Kroemer, RCA Rev. 17 (1956) 515. (451 M. Weinstein. R.O. Bell and A.A. Menna, J. Electrochem. Soc. 11 1 (1964) 674. [46] Zh.1. AlFerov, V.I. Korolkov and M.K. Trukan, Soviet Phys.-Solid State 8 (1967) 2813. (471 G. Zeidenbergs and R.L. Anderson, Solid-state Electron. 10 (1967) 113. [48] N.N. Gerasimenko. L.V. Lezheiko, E.V. Lyubopytova, L.V. Sharanova, A.Ya. Shik and V. Shmartsev, Soviet Phys.-Semicond. 15 (1981) 626.
195
196 Selected Works of Professor Herbert Kroemer 516
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1491 S.L. Wright, PhD Thesis, University of California, Santa Barbara, CA (1982). 1501 See, for example, C.M.Gamer, C.Y. Su, Y.D. Shen, C.S. Lee. G.L. Pearson, W.E. Spicer, D.D. Edwall, D. Miller and J.S. Hams, Jr., J. Appl. Phys. 50 (1979) 3383; see also the references quoted there. 1511 W.A. Harrison, E.A. Kraut, J.R. Waldrop and R.W. Grant, Phys. Rev. B18 (1978) 4402. [52] W.A. Harrison, in: Festkbrperprobleme/Advances in Solid State Physics, Vol. 17, Ed. H.J. Queisser (Vieweg, Braunschweig, 1977) p. 135. [53] W.A. Hamson. J. Vacuum Sci. Technol. 46 (1979) 1492. (54) S.L.Wright, M. Inada and H. Kroemer, J. Vacuum Sci. Technol. 21 (1982) 534. 1551 H.Kroemer, K.J.Polasko and S.L.Wright. Appl. Phys. Letters 36 (1980) 763. 1561 R. Kaplan, Surface Sci. 116 (1982) 104. 1571 W.A. Harrison, Surface Sci. 55 (1976) 1.
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H. Kroemer, "Barrier Control and Measurements: Abrupt Semiconductor Heterojunctions," J. Vac. Sci. Technol. B, Vol. 2(3), pp. 433-439, 1984. Copyright 1984, American Vacuum Society.
198 Selected Works of Professor Herbert Kroemer
Barrier control and measurements: Abrupt semiconductor heterojunctions Herbert Kroemer &partmentofEIectrical& Computer Engineering. Uniwrsityof Cali/ornia Sanra Barbam Ca!ifornia 93106
(Received 13 February 1984; accepted 18 March 1984) A brief critical review is given of diverse techniques used to measure heterojunction band lineups; they range from very reliable to worthless. Another problem pertains to the heterosystems themselves:Data on systems in which two semiconductors from a diaerent pair ofcolumns of the periodic table are combined, should be reviewed with suspicion, although some selected pairs are probably trustworthy-but none in which a compound semiconductor was grown on an elemental one. Technologies that do not lead to device-quality interfaces also probably do not yield devicequality lineup data. A l i t of the most trustworthy experimental data is given. The simplest possible theoretical framework for a theory of band lineups is a model of linear superpositon of atomiclike bulk potentials. Such a model automatically leads to a theory that is linear and transitive, in which the band lineups are orientation independent, and in which a technology dependence of the band lineups requires a technologydependent deviation of the atomic arrangement from the ideal one. The Harrison theory is both the simplest and the most successful theory of band lineups, although it still does not meet the needs of the device physicist. The set of most reliable data selected earlier agree very well with this theory, with a largest deviation of 0.18 eV and a standard deviation of 0.13 eV.
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PACS numbers: 73.40.Lq,73.30. y, 68.48.
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I. INTRODUCTION From a device physics point of view the most important aspect of a semiconductor heterointerface, and the point of departure for all subsequent considerations, is the lineup of the bands at the interface. These band lineups may vary over a wide range, from the most common struddling lineup of Fig. l(a)via the less common sruggered lineup of Fig. l(b),to the rare broken-gup lineup in Fig. I(c). The purpose of the present paper is to review the present status of our knowledge of those band lineups for the common diamond- and zinc-blende-type semiconductors, from both the experimental and the theoretical point of view. The paper draws heavily on two more extensive recent papers,’.’ to which frequent reference will be made. The first of these’ contains an extensive critique of various experimental methods that have been employed to determine band offsets, and of some of the ways in which nuisance effects such as spurious interface charges might falsify the apparent offsets. It also contains a discussion of technological problems that can make the (apparentor real) band offsetspoorly reproducible, especially in mixed-column heterosystems like Ge/GaAs. The second pape? selects from the large amount of experimental data those that are most likely to be correct, followed by a detailed review of various lineup theories. The selected experimental data are compared with the theoretical predictions, especially those of the Harrison atomic orbital (HAO) theory .’n4
II. EXPERIMENTALBAND LINEUPS A. Tho problem
To assess the validity of any theory of band lineups, it is necessary to compare its predictions with band offsets that
arealready known experimentallywith a degree of reliability sufficientto permit a meaningful test. Although the literature contains a very large number of lineup data for many different semiconductor pairs, few can be considered reliable enough to permit a meaningful test of lineup theories.’ For example, for the widely studied Ge/GaAs system, conduction band offsets ranging from 0.09 to 0.54 eV have been claimed in the literature, a range corresponding to 68% of the energy gap of Ge. Many of those values must be wrong, and this makes all data suspect. Ignoring ordinary measurements inaccuracies, one can identify four problem areas.
I. Indirect measurement techniques Many techniques that have been employed determine the band offsets only very indirectly, by projecting the results of whatever measurement is employed, upon a preconceived model of the heterojunction. If the model is not valid, the resulting offset values may be invalid, too. In particular,
-LJ.: . :.:
.,:.
a:.:
h
-1 .. ... J :.::...*..
’...‘.: ..
(a 1
....:,:. .:. (b)
......*..4 (C)
FIG. I. Band discontinuities a1 abrupt semiconductor hetcrojunctions. Three dilrent possibleband lineup arc shown: (a) “swaddling” lineup. (b) “staggered” lineup, and (c) “broken-gap”lineup. From Ref. 2.
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small residual interface charges tend to distort grossly the results of some measurement techniques. A critical assessment of various measurement techniques was given in Ref. 1 the results of which may be summarized as follows. Probably the most reliable data are those obtained from sufficiently carefully performed UPS or XPS photoemission experiments”on very thin heterojunctions, provided the heterojuncion itself was prepared by a technology yielding high structural perfection. A close second to UPS/XPS measurements are optical absorption (not emission!) measurements on multiquantum well structures.h Capacitance-voltage (CV ) measurements on heterojunctions may or may not bereliable, depending on the exact nature of the measurement. In fact, C-V profiling rhruugh an isotype heterojunction from an adjacent Schottky barrier’ is potentially one of the most reliable techniques. Least reliable are I-V measurements; many-but not all-are essentially worthless.’ This assessment is strikingly different from the situation with Schottky barriers.“ where I- Y and C-Y measurements are among the most reliable (and most widely used) techniques to determine Schottky barrier band lineups, ranking along with UPS/XPS techniques. The principal reason for this difference is the following: Heterointerfaces often contain non-negligible interface charges, which can grossly deform the band diagrams of the entire heterojunction and hence change most electrical properties of the structure.’ At a Schottky barrier, such charges are located right at the metal surface, where they are unable to deform the bands far away from the interface. On the other hand, two of the best heterojunction techniques. Dingle’s quantum well absorption technique: and C- Vprofiling through an isotype heterointerface: are fundamentally unusable to determine the band lineup at Schottky bamers.
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2. Technologyproblems The band offset data appear to depend somewhat on technological details of how the heterojunction is prepared. This dependence must reflect technology-dependent differences in the exact atomic arrangements near the interface. The exact nature of these differences (and their origin) is at present not understood. But it is clear that one cannot fully trust data that were taken on structures prepared under conditions significantly different from those employed for the highquality device structures whose lineups are the real object of the theory.
3. Chemically induced interface diporps Many heterojunctions that have been studied involve two semiconductors from different columns or column pairs of the periodic table, such as Ge/GaAs, Ge/ZnSe, GaAs/ ZnSe, InP/CdS, and many others. In all such systems, any interchanges of a t o m across the interface will introduce atomic dipole moments that change the band offsets. Such atom interchange effects can, in general, not be prevented. In fact, it has been shown9 that, for most crystallographic orientations, atom interchanges across the interface are necessury to prevent the accumulation of a huge interface-destabik i n g net interface charge. The final result will be an interface with both a residual interface dipole and a residual J. Vac. Sci. Technol. B, Vol. 2, No. 3, July-Sept. 1984
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interface charge, the magnitudes ofwhich depend sensitively on technology. These effects can be minimized by working with the electricallyneutral (1 10)cleavage planes of the compounds, and by growing the junction at a low temperature. But the latter is only a compromise, because the low-temperature growth tends to lead to poor bulk properties not representative of a device-quality semiconductor.
4. Antiphase disorder In heterojunctions between one of the column-IV elements and a I W V or a II/VI compound, severe antiphase disorder is likely to occur when the compound semiconductor is grown on the elemental semiconductor substrate, rather than in the opposite order.’.’ There probably does not exist a heterosystem more ill suited to a test of band lineup theories than GaAs grown on (001)-oriented Ge; yet this Combination has been one of the most widely studied-with predictably irreproducible results. In fact, recent work by N a v e et 01.’” has demonstrated that these structures do indeed suffer from heavy antiphase disorder. In my judgement, such compound-on-element systems should be expected nor to satisfy any simple lineup theory; only systems in which the element was grown upon the compound should be considered for testing such theories. 6. Reference systems for theory testing
When all these problems are taken into consideration, only two heterosystems remain that can truly serve as standards ofcomparison for lineup theories: The Al, Ga, - As/ GaAs system and the InAs/GaSb system. For the first of these, both superlattice absorption data6 and XPS data” for (IOO)-orientedabrupt heterojunctions show that the valence band offset is 15% & 3% of the direct energy gap at k = 0, both for x in the range 0.243,and for x z 1. If one assumes a linear relation with x , the data can be described by Ar, [Al,Ga, _xAs-GaAs] = (0.19 f0.04)~ eV, (1) where we have adopted the convention that Ar,,[ A-B J shall be positive if the band edge step is an upward step in going from A to B. Recent C-V profiling datai2 have confirmed the earlier band offset data. For InAs/GaSb, various data” show beyond any doubt that this system is of the broken-gap variety [Fig. I(c)],with a break in the gap of about 150 50 meV. Combined with the 300 K energy gap of InAs (0.36eV) this yields
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Arv [ InAs-GaSb] = (0.5I 0.05)eV. (2) The very unusual nature of this broken-gap lineup makes this system a severe test of any theory of heterojunction lineups. Compared to the (Al,Ga)As/GaAs and InAs/GaSb data, all other lineup data suffer from one uncertainty or another. The most likely to be reliable are the XPS/UPS data for lnAs on GaAsi4and for Ge on Si,” for which the following lineups have been reported: AP, [ InAs-GaAs] = - 0.17 eV, (3) Aru( G A i ] = - 0.2 eV. (41 The trouble with both systems is that they are badly lattice
200 Selected Works of Professor Herbert Kroemer 435
Herbert Kroomer: Barrlar control and meawremanfa
mismatched (7% and 4%). One must expect that the exact lineups depend on how exactly this mismatch is accommodated at the interface; hence they might be technology dependent. The Ge-on-Si value is subject to the additional criticism that the data were obtained on samples in which the Ge was grown at an unrepresentatively low temperature. As a result of these reservations, it is not clear how exactly the band offsets for both systems should agree with any theory that has made idealizing assumptions (even if implicitly) about the atomic structure of the interface and of the crystal adjacent to it. There exist large numbers of lineup data on heterojunctions in which the two semiconductors come from different columns of the periodic table. As was mentioned earlier, and discussed extensively in Refs. 1 and 2, all such systems are prone to exhibit technology-dependent interface charges and interface dipoles. These effects depend very strongly on the crystallographic orientation of the interface: The two least-suspect orientations are the ( 110) and (1 12) orientations.1.2.9.16.17 The widely used (001) and (111) orientations are highly nonideal for such systems, no matter how ideal they may be for III/Vsnly heterojunctions. Of all mixed-column lineup data in the literature the ones I consider least likely to suffer from complications are the XPS data of Kowalczyk ef ol.IRfor heterojunctions of ZnSe grown on GaAs ( 1 10)at 300 "C (nottheir 23 'C growth data):
[ZnSe on GaAs(1lo)] = 0.96 f 0.03 eV. (5) Finally, there exist numerous data in which elemental Si or Ge was grown on a compound semiconductor-not the other way around-which because of their growth sequence are not subject to the exclusion on the grounds of likely antiphase disorder, discussed earlier. Probably the least-suspect data on these element-on-compound systems are the XPS data, again of Kowalczyk ef a/.,'" for Ge grown on ZnSe(110): Ar, [ Ge on ZnSe(1lo)] = - (1.52 & 0.03)eV. (6) It is only with considerable reluctance that I inctude among the reference systems what is one of the most widely studied heterosystem, Ge on GaAs. The lineup data on this system scatter so widely" that it appears difficult to decide which of the data are least unreliable, and the strong chemical interaction of Ge with As makes the system prone to chemical interface reactions.2o However, recent data on MBE-grown Gesn-GaAs( 110)heterojunctions have tended to converge towards what appears to be the most carefully determined value, that of the Rockwell group.21
A r , [ Ge on GaAs(1lo)] = - (0.53 f0.03)eV,
(7)
obtained again by XPS,on junctions grown at 425 'C. C. Anlon correlation rule
There is strong independent evidence that in all systems such as (AI,Ga)As/GaAs and InAs/GaAq in which the anion atom species (As) on both sides of the heterojunction is the same, the valence band ofsets shauld be much smaller than the conduction band offsets.22This common onion rule arises from the theoretically wellntablished fact'' that the valence band wave functions derive largely from the anion J. Vac. Scl. Teohnol. E, Vol. 2,No. 3,July-Sept 1984
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atomic wave function. Taken together with the fact that the valence band wave functions tend to be more localized than the conduction band wave functions, this yields valence band energies that correlate strongly with the anion species. For semiconductor pairs with a common anion, the valence band offsets should therefore always be small compared to the conduction band offsets. For semiconductor pairs with the common cation X, the valence band energies at the interface should correlate with the different anion electronegativities. For the III/V compounds this implies E,,(XP) 300 000 cm’? s) two-dimensional electron gas in unintentionally doped InAs/AISb single 120 A quantum wells grown on GaAs substrat1:s by molecular beam epitaxy. Magnetoresistance and Hall measurements at T-0.4 K show a well-formed quantum Hall effect, with effects due to spin splitting observed at filling factors as high as Y = 17. The electron densities of these wells could be reduced by a factor 5 by using the negative persistent photoconductivity of these samples.
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Quantum well structure made from InAs, with barriers made from AISb, GaSb, or (A1,Ga)Sb alloys, possibly with the addition of As to the barrier, are natural candidates for the study of low-temperature magnetotransport effects such as the quantum Hall effect and the Shubnikov-de Haas effect. Of all binary III/V compounds, InAs has the second highest intrinsic electron mobility. Only InSb has a higher mobility, but it suffers from the absence of an approximately lattice-matched barrier material that would permit the construction of quantum wells with low-defect barrier interfaces, necessary for highest mobility transport. In the present work, we report on InAs quantum wells with straight (unalloyed) AlSb barriers, of the kind reported earlier by Tuttle et QZ.’.~ Although slightly less-well lattice matched and technologically slightly more difficult to grow than GaSb or (A1,Ga)Sb barriers, AlSb barriers have the advantage that they eliminate complications due to a broken-gap band structure at the interface. These complications are of interest in their own right, and were in fact recently studied by Munekata et ui.’ but in the present work it was desired to avoid them. Quantum wells of InAs/AlSb were first studied by ~ also reported the first observation of the Chang et u I . ,who quantum Hall effect in such structures. However, those early samples still suffered from relatively low mobilities ( 15 000 cm2/V s), and the transport measurements were made only down to T-4.2 K, so that much detail remained unresolved. In the years since the pioneering work of Chang er d.,great improvements in the technology of the InAs/AISb have been made. Low-temperature ( < l o K ) mobilities up to 330000 c m 2 / V s were reported by Tuttle et aZ.* in 1989, and more recently, a value as high as 613 000 c m 2 N s has been reported by Chalmers et a[.* in a quantum well with a modified interface structure. The work reported here is a continuation of the earlier work of Tuttle et al., drawing on the same high-mobility samples, and extending the magnetotransport measurements down
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”Current address: Materials Department, University of California, Santa Barbara, CA 93106.
1428
Appl. Phys. Lett. 58 (13),1 April 1991
T-0.4 K. More specifically, we report on low-temperat !re magnetoresistance and Hall effect data on two 120 A InAs/ AlSb quantum well samples, with the magnetic field applied perpendicularly and parallel to the plane of the electron layer. Theiie data provide evidence for a high quality, high-mobility, two-dimensional electron gas layer in these wells. The unintentionally doped 120 ,& InAs/AISb samples discussed in the present letter were grown by molecular beam epitaxy on GaAs substrates, with InSb-like quantum well interfaces, as described by Tuttle el a/.’ Because of the between the InAs/AISb system and lattice mismatch (:I%) GaAs, we expect the samples to have threading dislocation densities of lo7 cm- or higher,‘ and one of the objectives of this study was tci see if these dislocations posed a serious obstacle in obtaining high-quality two-dimensional (2D) transport. Hall bars ( 7 x 3 mm’) with three pairs of Hall voltage probes were photolithographically defined, and contacts were made to the electron gas by alloying dots of indium at 300°C for 5-10 min. The samples were immersed in He-3 to temperatures T-0.4 K, and measured in magnetic fields to 23 T at the Francis Bitter National Magnet Laboratory. Transverse magnetoresistance and Hall effect measurements were taken with the applied magnetic field 3 perpendicular to the plane of the electron layer. The two dktinct magnetoresistance measurements with B i n the plane of the electron layer were taken, with B parallel and perpendicular to the current. All resistance measurements were taken using low-frequency (typically 11 Hz)ac lock-in techniques; the current bias levels ( 1988 A m e x a n lnslltute of Phys:cs
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soA W
I
SamWlS i
s cap
I
Sam&
2
FIG. 1. Samples used to study the effectof the superidtticc period on dislocation properties. To facilitate comparison, the three superlattice packets contain the same amount of GaAs and Al,, Ga,, As in each packet.
,
reduction would have taken place even for a non-SLS Suffer layer of the same thickness. Four samples were grown. In sample No. 1 (Fig. I ), the structure, grown at 630 “C,consisted of three superlattice (SL)“packets,” laFled SL Nos. 1,2, and 3, separated from each other by 250 A of Ale,, Ga,,As barriers. To facilitate comparison, each of the three SL packets contained the .~urn? amount of GaAs and Al,,., G%., As. In SE Nob1, the 3050-A packet was partitioned into15 periods of I00 A of GaAs and 100 A of Alo.,G%.,As. In SL No. ,: the same amountyas partitioned into 30 periods of 50 A of GaAs and 50 of AI,,Ga,,,As. Finally, in SL No. 3, 60 periods of 25 A of GaAs and 25 A of Alo,3G%,,As constituted the 3000-Alayer. To account for a possible attenuation ofthe dislocation density with increasing distance from the interface, sample No. 2 was prepared (Fig. 1 ). It had the same growth param eters and buffer layers as sample No. 1, the only difference being that the stacking sequence of the three SL packets was reversed. A control sample, No. 3, was also prepared on a GaAs ( 2 f l B ) substrate. A11 the growth parameters were kept the same as in other growths, and the same stacking sequenceof the SL packets as in sample No. 1 was employed. Only the SLS buffer was omitted from this control sample (Fig. 1 ). Finally, an “ordinary” double hererostructure sample (No. 4, not shown in Fig. 1 ) was also prepared, which con-
4
681 1
J. Appl. Phys.. Vol. 64, No. 12.15 December 1968
FIG. 2. Typical low-temperature cathodoluminewence (CL) spectra. ( a ) Spcctnini recorded front the 1ow-dis)ocution-density reference samplc No. 3, grown on a GaAs suhstratc. The decrease in the luminescence intensity towards shorter SL period is a characteristic behavior ofun increase in interface recombination velocity. ( b ) A typical low-temperature CL spectrum from sampie No. 1. A trend opposite to sample KO,3 is cvident.
sisted of a!hic& 5000-A GaAs region sandwiched between two 2500-A AI,, Gao,,As barrier regions. Lcw-temperature CL measurements were used to assess the quality of the differezt SL packets. They were carried out in a modified JEOL STEM model 200 equipped with a liquid-helium stage. A relatively low-energy ( 150-keV) electron beam was used, to avoid formation of radiation-induced damage to the material during the observation. No correction to the system transfer fiinction was appIied to the collected data. To take into acccunt any complications due to the fact that photons from the three SL packets have digererent escape depths, the cathodoluminescence was also monitored from the substrate side of t.he sample. To this end the silicon sub strates of both samples No. 1 and No. 2 were thinned down and dimpled to within tens of microns away from the epitaxbal layers. k hot aqueocs solution of 20% potassium hydrcxideaf 120 “Cwas used as a highly selectiveetch to remove the dimpled silicon region until the epitaxial GaAs layer was exposed.Cathodoluminescence measurements were done on both the epitaxial sides and the substrate sides of both samples. Figure 2 ( a ) shows a typical spectrum from the control sample. One can clearly identify the three peaks corresponding to the 1W-, jO-, a d the 25-A SLs. As can be seen from Fig. 2(a), there exists a trend in which the CL intensity Liu, Petroff, and Kroemsr
681 1
Selected Works of Professor Herbert Kroemer decrcmes as the S L period decreases. This is probably due to an increase in the recombination at the increased riumber of interfaces or-more likely-inside the (A1,Ga)As barriers, as the SL period decreases. la*‘l Figure 2(b) shows a spectrum taken from the epitaxial side of sample No. I, with the CL peaks from the three SLs labeled. The ~ u m i n ~ ndata c e from the substrate side were essentially identical to those from the epitaxial side, indicating that the intensity trends seen cannot be due to differences in photon escape. Figure 3( a) illustrates the normalized CL peak intensities of sample No. I as a function of SL period. The n o ~ ~ ~ ~ ais tdone j o by n simply taking the ratio of the heights of the line peaks in sampk No. 2 to those in the control sample No. 3. No attempt was made to integrate over the broadened lines. The error bars indicate the spread of data due to (a) spatial variations of relative intensity an the same side and (b) differences in relative intensity on different sides of the same sample. The trend, evident in Figs. 2 and 3(a), is just the opposite of ?hat one can observe ir, the control sample. The 25 A + 25 A SL recovers to about 20% of the intensity of the corresponding SL grown on a GaAs substrate, despite the fact that cross-sectional TEM data indicate that all three SL packets have didocation densities in the mid-107-cm range. An additional data point has been A, corresponding to the intensity appended to Fig. 3, at 5 from the “ordinary” double heterostrueture of sample No. 4. Clearly, in sample No.1 the luminescence intensity incmuscs very strongly as the well width decreases. One might be tempted to explain such an observation in terms of a reduction of the dislocation density away from the GaAshilicon interface, even though TEM measurements (on other samples; we do not have TEM data on sample No. 1 itself)
-’
show only a very slight decrease in dislocation density, totally insufficient to explain the extremeiy strong luminescence trend. Such an explanation is fully ruled out by the data of sample No. 2, for which the normalized CL intensity from sample No. 2 is shown in Fig. 3( b). One can see the same basic trend as in sample No. 1, in which the narrow-well ( 100-A) stnlcture. As shown in Fig. 2(b), the spectra of the dislocated samples exhibit complex line-brcadening effects. At least part of this broadening is evidently the result of the presence of strong spatial inhomogeneities, which were clearly visible in spectrally resolved CL images, as in Fig. 4. The images shown were formed at exactly the same location, but using different wavelengths to image the different SL packets. One can readily see an ixrease in nonunifcrmity as the SI, period decreases. This is what one would expect if the inhomogeneities were simply due to spatially varying well thic.knesses. The origin of these variations is not clear, nor is it clear to what extent they might be related to the diferences between samples Nos. 1 and 2. In fact, it is not even certain that these inhomogeneities have anything at all to do with the growth on a lattice-mismatched substrate: some inhomogeneities have been observed even in the quantum-well luminescence in low-dislocation structures grown on GaAs substrates.'' DlSCUSSlON The nonradiative recombination effects associated with dislocations have been attributed to several different possible causes. The most likely possibility is chat the recombination centers are associated with deep levels due to unreconstructed dangling bonds along the dislocation cores. It was shown by Kirnerling and Pateli3that most of the dangling bonds at the dislocation cores in silicon are reconstructed or rearranged so that only a small fraction of the sites are electrically active. The authors estimated a 2.5% site occupation in the Shock1ey"dangling-bond structure or a 1% site occupation in the Hirsch" dissociated dislocation model. Defectsite spacings of the order of 200 A along the dislocation core were measured. In zinc-blende semiconductors, the situation is anticipated to be similar. Kimerling and Patel proposed that the electrically active sites are located at the dislocation kinksites that are associated with dislocation motions from one Peierls valley to the other in the same glide plane. These kinks are known to he highly mobile along the dislocdtion core. Their motion is easily thermally activated at the growth temperature. If one accepts the kink model of recombination at dislocations, the simplest explanation of our observations woufd be that in sufficiently narrow-well superlattices the overwhelming majority of dislocation kinks are somehow expelied from the GaAs porrion of the SL structures into ihe (A1,Ga)As barriers. Conceivably, the strong electric fields that are present at heterointerfaces, or even chemical potential gradient, might play a role. Recombination-enhanced kink migration due to minority-carrier generation during the CL observation is unlikely, since no change in the luninescence yield of the material has been observed as a function of time. Whatever the mechanism, any spatial expillsion mechanism would clearly run much closer ro completion in narrow-well structures than in wide-well ones. Further experiments are needed to clarify theexact mechaiiism. Several such experiments-suggested by several possible mechanisms-are currently in preparation. One alternate to dislocation kinks a5 the recombination 6813
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centers would be the Co:treN utmosphere of native point defects surrounding t.he dislocation cores. There are a variety of ways in which native point defects can be created around the dislocation cores. For example, when a dislocaticn jog moves from one glide plane to an adjacent one, a row of vacancies or interstitiah results, depending on the direction of motion. At the typical growth temperature of the GaAs epitaxial layer (580-53C "C) dislocatians are highly mobile. Depending 011 the nature of the point defects, the latter may be singly or mu!tiply charged, or remain neutral. Such defects can induce deep trap states in the gap region and are thus electrically active. A less likely possibility than either dislocation kinks cr dis!ocation-associated native defects would be chemical impurities that are trapped along the dislocation cores. Impurities have been observed to diffuse along dislocations (by pipe diffusion) in semiconductors. However, oye do not believe that this is a likely mechanism: Many different kinds of devices have operated successfully in GaAs/( A1,Ga)As heterostructures grown an Si substrates, and if extensive pipe diflusion were a problem, this would almost certainly have been noticed, particularly when one considers that such material typically conteins dislocation density of the order of 108 c m . ~2 Ih ~
The various driving forces eliscussed above for the spatial expulsion of dislocation kinks from the quantum wells could also be invoked for a point defect or an impurity model of the recombination at dislocations. Finally, an alternate to the spatial expulsion of the energy states responsible for tire recombination activity might be an energetic expulsion of the associated energy levels from the forbidden energy gap into the conduction band and/or the valence band, thus rendering the recornbination centers ineffective. It has been shown" that, theoretically at least, a deep t.rap in the bulk can become 2 shallow energy state at a heterointerface and uice versa. The effeci of an interface is essentially to shift thes-like energy level and to split the rhrre p-like levels, with thep-like state that points in the direction perpendicular to the interface being affected most. However, we find this-or any other-energetic expulsion model least likely: Deep levels tend M be highly localized, extending over only a few atomic distances. Hence one would expect an efficient energetic expalsion only for quantum wells that are only a few atoms wide. li is hard to see how a two-orders-ofmagnitude increase in CL intensity could resul; already for wells that are still 50 A wide. In summary, we have shown that in a sufficiently shortperiod superlattice in a heavily dislocated material, strong interaction exists between the recombination centers and the superlattices so that the effective recombination rate is highly reduced. The interaciion is a strong function of the superlattice period. The origin of such an interaction is likely to be a spatial expulsior. of dislocation-related recombination centers from the well portion of the superlattices into the barriers, driven by either electricel or chemical forces. These results strongly suggest that minority-carrier devices in GaAs on silicon substrates should exhibit a superior performance if the active part of the devices is composed of a narrow GaAs quantum weli. Liu, Petroff, and Kroemer
68'13
322 Selected Works of Professor Herbert Kroemer ACKNOWLEDGMENT
We wish to express our appreciation to the Army Research Office for supporting this work. 'P. M. Petrof, in Semiconductorsand Insulators. editcd by F.C. Brow and N. lroh (Gordon and Breach, New York, 1983 1, Vol. 5, p. 307. 'H.Z. Chen, A. Ghaffari, H. Wang, H. Morkoq. and A. Yariv, Appl. Phys. Lett. 51.1320 (19S7). 'G. Griffiths, K. Mohammed, 9. Subbanna, H.Kroemer, and J. L. Merz, Appl. Phys Lett. 43, !059 (1983). "J. S. Ahearn and P. Uppal (personal communication). 'S. L. Wright, M.Inada, and H.Kroemer, J. Yac. Sci. Techno!. 21, 534 (1982).
"P.Uppal and K.Kroemer, J. Vac. Sci. 'I'echnol. B 4,641 (1986). 7S. L. Wright and H. Kroemer, Appl. Phys. Lett. 36, 210 (1980). "z. L. Weber, E. R. Weber, J. Washburn, T. Y.Liu, and H. Kroemer, in Heremepiruxy on Silicon I i 9Yol. 91 of Malerials Research Sofiety S y m p
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sium Pmceedings, edited by J. C. C. Fan, J. M. Phillips, and B. Y.Tsaur Material Research Societv. 11. 9 1. .. Pittsbureh. 19871..~ 'J. S. Ahedrn, P. Uppal, T. Y. Liu, and H. Kroemer, J. Yac. Sci. Technol. B 5., 1156 11987). . . "'G. Duggan, H. I. Ralph, and R. 3. Elliott, Solid State Commun. 56, 17 (1985). "8.Serniage, h4. F. Prrcira, F. Alexandre, J. Beerens, R. Azoulay. C.Tallot, A. M. Jeanlans, and D. Mrchenin, J. Phys. (Paris) Colloq. 48, C5-135 (1987). "P. M. Petroff, R. C. Miller, A. C. Gossard, and W. Wiegmann, Appl. Phys. Lett. 44,217 (1984). "L. C. Kimerling and J. K.Patel, VLSI Electron. 12, 223 (1985). I4W. Shockley, Phys. Rev. 91, 228 (1953). "P. B. Mirsch, J. Phys. (Paris) Colloq. 40,C6-27 (1979). 'OM. M. Al-Jassim, A. E. Blakeslee, K. M. Jones. and S. E. Asher, Inst. Phys. Cnnf. Ser. No. 87,99 (19x7). "R. E. Allen. 1. P. Buisson. and J. D. Dow, Appl. Ptays. Lett. 39, 975 (1981 ). I
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Reprinted Articles
Reprinted from H. Kroemer, T.-Y. Liu, and P. M. Petroff, "GaAs on Si, and Related Systems: Problems and Prospects,'' J. Cryst. Growth, Vol. 95, pp. 96-102,1989. Copyright 1989, with permission from Elsevier.
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Selected Works of Professor Herbert Kroemer .lourn;il o f Crystal Growth 95 ( I Y X 9 ) Yh-102 North-Holland. .Am~ierd;iiii
96
GaAs ON Si AND RELATED SYSTEMS: PROBLEMS AND PROSPECTS
The dominant problem in the epitaxial growth o f GaAs and other I I I L V con1pc)unda (111 sIIicon I \ the prohleni of threading dislocations caused by the large lattice mismatch of thc compound seniicciiiductorr rrlntlve t o the SI whstrate. Effort3 to rupprcss these dislocations to levels a s low as arc routinely achieved in epilaxy o n lattice-matched ruhstratcr. hiivc fiillcn far short o f the goal. and there are strong theoretical arguments againsl this pohaihility. However. proniismg device5 are being achieved dehpite the high dislocation densities. even demanding minority carrier device.r w c h ii?, q u a n t u m well lasers. Dlslocatlonr threading throuph narrou quantum wclls art- evidently far less deleterious than hulk dislocations. Thc prospect\ for VI.SI IiBT circuits arc' iilso promi\ing.
1. Introduction
Very impressive progress continues to be made in the performance of GaAs/(Al,Ga)As and other coinpound semiconductor devices grown on Si substrates, by MBE or OMVPE. Probably nothing illustrates this better than the achievement, by several groups. of cu' lasers with non-negligible operating lifetimes [I ,2]. Considering that cw lasers are more demanding of crystal quality than any other device. this progress is certainly gratifying. But serious questions remain. Put bluntly. we d o not really understand why the material works as well as it does. and in order to reach the limits of its capability. such an understanding will almost certainly be necessary. There are (at least) two quite different kinds of problems : ( a ) The most urgent problem is the misfit threading dislocation problem. caused by the 4%, lattice mismatch between Si and GaAs. In the best material grown to date. the dislocation densities are still above 10' cm-', more often in the l o 7 c m - 2 range. In bulk. such material would be essentially useless. Nevertheless, it i s in such material that room-temperature cw lasers with
non-negligible operating lifetimes h a v e been achieved. ( b ) A second problem is the site allocation problem. that is, t h e problem of which of the t w o fcc sublattices of the Si crystal becomes the Cia sublattice. and which becomes the As sublattice [3.4]. and how confusion in this site allocation is avoided. The present paper concentrates on the dislocation problem. B u t we continue to be puzzled by the site allocation problem. In the early days of GaAs-on-Si technology, i t was believed by somc -. including one of the present writers (51 - that growth o n the favored (100) orientation was bound t o lead to heavy antiphase disorder. Fortunately. this problem was easily overcome by simple misorienting the Si substrate slightly [ 6 ] ,but it is still not clear why this simple recipe works!. One explanation was that the substrate preparation led to a Si surface i n which all terraces belonged t o the same sublattice [3.7]. but recent data have clearly shown that n o t even that is necessary [8-101. The mystery i h further deepened by the observation that both of the two possible sublattice allocations are achievable without antiphase disorder. depending on the nucleation conditions (6.8,Y.l I]. However. wen if the site allocation problem
0022-0248/89/$03.50 C Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Reprinted Articles H. Kroemer et ul. / GaAs on Si and relatedsystems:problems andprospecrs
remains a fascinating scientific puzzle, it does not appear to pose a serious problem from the device performance point of view. For this reason, the remainder of this paper concentrates o n the dislocation problem.
2. The threading dislocation problem The lattice constant of GaAs is about 4% larger than that of Si. In epilayers of the kind of thickness required for almost all devices, the mismatch leads to the formation of misfit dislocation at or near the interface, running (ideally) parallel to the interface. A 4% misfit requires a dislocation roughly every 25 atomic rows. The relevant Burgers vector have the (110) directions, with a magnitude a / f i 4 A, where a is the lattice constant. That is, there must be two orthogonal dislocation networks with a spacing between dislocations in For a variety each network of roughly S = 100 of reasons, these dislocations do not stay confined near the vicinity of the interface, but bend upwards into the substrate, where they form threading dislocations (recall that a dislocation cannot end inside the crystal, but only on its surface). If each dislocation remained confined for a length L , the density D of (primary) threading dislocations would be
-
A.
where the factor 4 arises from the fact that there are two orthogonal misfit dislocation networks, and each dislocation has two ends. It is not well understood what controls the confinement length, and a discussion of this topic is outside the scope of this paper, but empirically, typical confinement lengths are less than 1 pm. Assuming, for simplicity. L = 1 pm, yields D = 4 X 10’” cm-’, a huge density. To achieve a primary threading dislocation density comparable to bulk material, say, lo4 cm-’, would require confinement lengths of the order 400 cm! Evidently, in order to achieve dislocation densities sufficiently low to make the material useable for devices, the overwhelming majority of the primary dislocation must be an-
325 97
nihilated by recombination of pairs of threading dislocations. To a considerable extent, such annihilation takes place naturally as the epitaxial layer grows thicker. Whenever the surface ends of two threading dislocations with the same Burgers vector approach each other, they may recombine, and that leads to a rapid thinning-out of the dislocations as the epitaxial layer grows thicker. If it were feasible to grow sufficiently thick epitaxial layers, very low dislocation densities would presumably result [ 121. Unfortunately, very thick buffer layers are ruled out in the case of GaAs-on-Si by the large difference in thermal expansion coefficient between Si and GaAs, which caused a large tensile strain to be built into the epilayer during cooling from the growth temperature. As a result, GaAs epilayers thicker than about 4 p m tend to exhibit massive cracking. The question then is what dislocation densities can be achieved within about 1-2 pm from the Si intelface, leaving about 2-3 pm for the device itself. In the absence of any specific dislocation suppression schemes, but under otherwise “good” growth conditions, one find dislocation densities as low as 10’ cm-* at such distances, about four orders of magnitude higher than routine values for GaAs-on-GaAs growth.
3. Dislocation reduction schemes
There have been a large number of attempt in recent years to d o reduce the threading dislocation densities, by various kinds of buffer layers. especially strained-layer superlattice buffers [13]. Although drastic improvements are often claimed, in the last analysis all these efforts have fallen far short of bridging a gap some four orders of magnitude wide, and they are more remarkable for what they have failed to achieve than for what they have achieved: Improvements in dislocation density by a factor of two, compared to doing nothing at all, while hailed as improvements, are simply uninteresting, and even the best results have given not much more than a factor of ten in improvement, leading to dislocation densities around lo7 cm-2, still several orders of magnitude too high to meet the goal of “bulk-quality’’ material. This
326 Selected Works of Professor Herbert Kroemer
failure of the SLSL buffer layer approach came as a surprise t o many investigators (including this writer. who had attempted t o use this approach). because SLSL layers had been remarkably effective in suppression of threading dislocations at lower dislocation densities. El Masry et 31. [I41 have recently proposed that dislocation tangling at high dislocation densities places a natural upper limit to the dislocation densities that can be suppressed by SLSL buffer layers. As a result o f statistical fluctuations. these authors found that although there tend to occur regions several vim i n diameter that tend to be dislocation-free. the dislocation density outside these islands tends to more than make up for the reduction. leading t o undiminshed average dislocation densities. We ourselves have performed work along the same lines as El Masry et al.. with essentially the same results [ 151. The best (or better: least-bad) results have been achieved by a technique that conies closes^ to doing nothing spectacular at all: A simple hightemperature anneal of the epilayer [16]; which reliably. seems to yield values around 10' cm What appears to be the best (believable) result reported in the literature was achieved by a bruteforce extension o f the thermal anneal technique: Using a sequence o f 13 in-situ anneal steps ;it 800°C alternating with OMVPE growth. I t o h et al. [17] were able to reduce the dislocation density to between 2 X 10' and 5 X 10" cm *. Barring any major unexpected breakthroughs. i t is hard to see how any of these approaches can lead to material o f "bulk-quality". Perhaps the only major hope that is left is to work deliberately with small islands of material. Initial results i n this direction. in the (Ga.ln)As/GaAs system [l X I are promising, but i t remains to be seen how successful this approach will ultimately be.
'
4. Model for annihilation kinetics of threading dislocations I n order to understand better the fundamental reasons for the failure t o achieve the desired dislocation suppression, i t is instructive to model this problem mathematically.
Let D ( . Y )he the areal density (number per u n i t area) of threading dislocations. The rate at which dislocationa disappear by recom bi nation wi I I then he proportional to the square of their concentration. iis for other hiniiry reconibination laws. d D / ' d s = -AD'.
(2)
where X is an unknown proportionality factor of the dimension of ;I length. Integration o f (2)yields
whcrc D ( 0 ) is the primary threading dislocation density. and where the asymptotic limit refers t o the situation sufficiently far from the interface t ti a t the i n a.1o r i ty 1) f d islocat ions has recoin b i ned . Empirically. one finds between 10' a n d dislocations per cm.' at a distance of about 1 pin. iniplying a valuc of X between 10 ' and 10 cni. The asymptotic behavior in (3)haa a number o f important consequtmces: ( a ) The first o f these is that the asymptotic density iit ;I given distance is independent of the initial density. T h i a nicans that a n y reduction in the primary threading dislocation density. hy whatever means. will not lead t o a proportional reduction i n the asymptotic density. unless the prin7uq dislocation density is reduced all the way to the desired final value! I t a l x ) explains. for example. why the quality o f . say. CinSb/AISb structures grown on Si i h no poorer than that of GaAs/AIAs structures. despite a much larger lattice mismatch. ( b ) The second consequence is that the decay of the dislocation density is n o t exponential. but o n l y inverse linear. What this means that any initial reduction o f the dislocation density by ;I large factor, achieved by the incorporation of ii suitable buffer layer. will n o t lead t o a further reduction by the same factor by simple doubling the buffer layer. To achieve the desired reduction in dislocation density by the desired factor o f 10' o r more clearly then calls f o r an increase in t h e capture crosssection and hence a n increase i n the characteristic length h by the same factor. I t ia hard t o see how this can be achieved.
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5. Dislocations in quantum wells
%
As stated above, the best material to date still has threading dislocation densities in the range between 10‘ and lo7cm-’, or more, as established by transmission electron microscopy. Nevertheless. room-temperature cw quantum well lasers have been demonstrated in such material. On the other hand, no room-temperature cw operation has been reported for “ordinary” double heterostructure lasers made from such material. This suggests that superlattices or quantum wells might drastically modify the electronic properties of dislocations in such a way as to make them far less deleterious. There are other observations pointing in the same direction. For example. in our own extensive earlier work on the photoluminescence properties of GaSb/AISb multi-quantum well superlattices grown on grossly lattice-mismatched GaAs substrates [19], we had found excellent photoluminescence properties, initially suggesting that the dislocations had been suppressed by the first-grown portion of the superlattice, adjacent to the GaAs substrate. However, TEM studies subsequently showed that no such suppression had taken place [20], and that the threading dislocation density was in fact very high, about 10’ cm-’. Prompted by such considerations, we have performed a series of experiments designed to look at the luminescence properties of heavily dislocated epitaxial layers of GaAs grown by MBE on Si substrates, each layer containing three superlattice “packets” with different superlattice periods 1211. Three samples were grown by MBE, all at 630 O C, all on (21 1)-oriented substrates. Each contained three superlattice (SL) “packets”, labeled S L # l , # 2 and #3, separated from each other by 250 A of AlO,,GaO,,As barriers. Each of the three SL packets contained the same amount of GaAs and AI,,Ga,,,As. In S L # l , the 3000 packet was partitioned into 15 periods of 100 of GaAs and 100 A of Al,,Ga,,As. In SL#2, the same amount was partitioned into 30 periods of 50 + 50 A. Finally, S L # 3 consisted of 60 periods of 25 -+ 25 A. Samples # l and # 2 were both grown on Si substrates; the only (intentional) difference being the order of the three superlattice
A A
A
A
101
lo2
99
id
104
Well Thickness [A1
Fig. 1. Cathodoluminescence intensity of GaAs/(AI.Ga)As superlattices with various well widths. grown on Si suhstrates. relative to identical superlattices grown on GaAs substrates.
stacks: In sample # I . the 100 A + 100 SL was closest to the substrate and the 25 A 25 SL was farthest away: in sample # 2 the stacking order was reversed. Sample # 3 was a control sample, with the same stacking order and growth parameters as sample # l . but on a GaAs rather than a Si substrate. An “ordinary” double heterostructure sample was also prepared, consisting of a thick 5000 GaAs region sandwiched between two 2500 AI,,.,Ga,,As barrier regions. on a Si substrate. Low-temperature cathodoluminescence (CL) measurements were used to assess the quality of the different SL packets. To eliminate any uncertainties due to the fact that photons from the three SL packets have different escape depths, the cathodoluminescence was also monitored from the substrate side at least of samples #1 and #2, after removing the Si substrates with a KOH etch until the epitaxial GaAs layer was exposed. Fig. 1 illustrates the normalized CL peak intensities of sample # 1 and #2 as a function of SL period. The normalization is done by simply taking the ratio of the heighrs of the line peaks in samples # 1 and # 2 to those in the control sample #3. N o attempt was made to integrate over the broadened lines. The error bars indicate the spread of data due to (a) spatial variations of relative intensity on the same side, and (b) differences in relative intensity on different sides of
+
A
A
328 Selected Works of Professor Herbert Kroemer
the same sample. The trend speaks for itself: Althcrugh the luminescence of the 100 + 100 A SL remains poor, that of the 25 + 25 A SL has recovered to about 20% of the intensity of the corresponding SL grown on a GaAs substrate. despite the fact that cross-sectional TEM data indicate that all three SL packets have dislocation densities in the mid-107 cm-’ range. not decreasing significantly from the bottom SL packet to th,e top packet. The additional data point at 5000 A corresponds to the intensity from the “ordinary“ double hetero-structure sample, showing the very poor luminescence for that sample. Clearly, the luminescence intensity increases very strongly as the well width decreases. for essentially fixed dislocation densities, indicating a drastic reduction in the undesirable recombination efficiency of the dislocations in narrow quantum wells. The most likely explanation is that the recombination centers are associated with deep levels due to unreconstructed dangling bonds along the dislocation cores. It was shown by Kimerling and Patel [22] that in silicon only a small fraction of the sites at the dislocation cores are electrically active. Defect site spacings of the order of 200 A along the dislocation core were estimated. In zincblende semiconductors, the situation is expected to be similar. Kimerling and Patel proposed that the electrically active sites are located at the dislocation kink sites that are associated with dislocation motion within their glide plane. These kinks are known to be highly mobile along the dislocation core, and their motion is easily thermally activated at the growth temperature. I f one accepts the kink model of recombination at dislocations, the simplest explanation of our observations would be that in sufficiently narrowwell superlattices the overwhelming majority of dislocation kinks are somehow expelled from the GaAs portion of the SL structures into the (A1,Ga)As barriers. Conceivably, the strong electric fields that are present at hetero-interfaces, or chemical potential gradients, might play a role. For a discussion of alternate possible mechanisms, considered !ess likely, the reader is referred to our original paper [23].
A
A
Whatever the exact mechanism. we believe that o u r our results explain the surprisingly good performance of GaAs/(Al.Ga)As quantum well lasers grown on Si substrates. as opposed to “ordinary” double heterostructure lasers. Going beyond that. our results strongly suggest that minority carrier devices in GaAs on cilicon substrates should quite generally exhibit a performance approaching that of devices grown o n GaAs substrates whenewr the active part of the devices is can be constructed from narrow GaAs quantum wells. or narrow-well superlatt ices.
6. Dislocations in heterostructure bipolar transistors The situation in heterostructure bipolar transistors (HBTs) is quite different than in quantum well lasers, because the incorporation of superlattices in the base region is not practical. However. we come to a similarly positive assessment. for quite different reasons. In fact. HBTs with remarkably good properties made from (Al,Ga)As/GaAs on Si substrates have already been demonstrated [23], despite the fact that the epi-layers o f GaAs on Si typically probably had threading dislocation densities exceeding lO’cm The central issue in an HBT is the competition between minority carrier capture by a dislocation and capture by the collector depletion layer: The worst a dislocation can d o in the base of an HBT is to act as a perfect sink for minority carriers. But if the nearest dislocation is farther away from an injected carrier than the collector depletion layer, that carrier is more likely to be collected by the collector than to be captured by a dislocation. In many HBTs there is a built-in field driving the carriers towards the collector [24]; this would reduce the capture by dislocations further. Even neglecting such fields, but assuming that dislocation lines run perpendicular to the base plane, one estimates a capture cross section of about v w 2 , where w is the base width. If D is the dislocation density, then. for uniform carrier injection by the emitter, one estimates that the fraction
’.
f, = rrDw’
(4)
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GuAr on SI and related systems problems and prospecrs
of the injected carriers is captured by dislocations. Assuming D = lo7 cm-2 (as a typical value for GaAs on Si) and w = lo-’ cm (as a typical value for HBTs), one predicts a surprisingly low capture fraction of about 0.38, essentially negligible - at least for discrete transistors with a large enough area A ( A >> 1 / D ) that there are several dislocations present per device. The argument becomes more complicated for VLSI circuits with very small devices. Emitter areas A as small as (1 pm)’= lo-‘ cmz can be anticipated. For dislocation densities D I lo7 cm-*, over 90% of the transistors would have no dislocations at all, however, the remaining transistors would be influenced proportionately more strongly: Transistors threaded by a single dislocations would lose 3% of the injected carriers rather than only 0.3%. This is still an essentially negligible loss, but in a sufficiently large VLSI circuit, there will always be some transistors threaded by several dislocations, with proportionately larger losses. For discrete devices, a very small fraction of transistors with unacceptably high losses would represent an inconsequentially small reduction of the manufacturing yield, but in a VLSI circuit they would jeopardize the entire circuit. To the first order, one might expect that the threading dislocations are randomly ( = Poisson) distributed, implying a probability
m N N!
P(N)=-
e- 10%). From (4), for ( N ) = A D = 0.1, we find P(4) - 4 X Evidently, under our assumptions, serious yield problems would arise only for circuits with more than about lo’ transistors. Inasmuch as circuits of this size should be anticipated, the problem is not negligible. But is is also evident that even a small reduction in dislocation density, or an increased tolerance of the individual device to dislocations, would all but alleviate the remaining threat.
101
Acknowledgements This work was supported by the US Army Research Office.
References [l] D.W. Nam, N . Holonyak. K.C. Hsieh. R.W. Kaliski. J.W. Lee. H. Shichijo, J.E. Epler. R.D. Burnham and T.L. Paoli, Appl. Phys. Letters 51 (1987) 39. [2] H.Z. Chen, A. Ghaffari. H. Wang. H. Morkoq and A. Yariv, Appl. Phys. Letters 51 (1987) 1320. [3] H. Kroemer. J . Crystal Growth 81 (19x7) 193. [4] H. Kroemer. in: Proc. 14th Intern. Symp. on GaAs and Related Compounds, Heraklion, Crew. 1987. Inst. Phys. Conf. Ser. 91. Eds. A. Christou and H.S. Rupprecht (Inst. Phys.. London-Bristol, 1988) p. 21. [ 5 ] For a 1986 review o f this topic. see H. Kroemer. in: Heteroepitaxy on Silicon. Eds. J.C.C. Fan and J.M. Poate. Materials Research Society Symposia Proceedings 67 (Mater. Res. Soc.. Pittsburgh, PA. 1986) p. 3. 161 R.J. Fischer. N.C. Chand, W.F. Kopp. H. Morkq. L.P. Erickson and R. Youngman. Appl. Phys. Letters 47 (1985) 397; see also R.J. Fischer. H. Morkoq. D.A. Neumann. N. Otsuka. M. Longerbone and L.P. Erickson. J. Appl. Phys. 60 (1986) 1640. [7] D.E. Aspnes and J. Ihm. Phys. Rev. Letters 57 (1986) 3054. [8] P.R. Pukite and P.I. Cohen. J. Crystal Growth 81 (1987) 214. [9] P.R. Pukite and P.I. Cohen, Appl. Phys. Letters 50 (1987) 1739. [lo] K. Kawahe and T. Ueda. Japan. J. Appl. Phys. 26 (1987) L944. Ill] K. Kawabe. T. Ueda and H. Takasugi. Japan. J. Appl. Phys. 26 (1987) L114. 1121 See. for example. G.H. Olsen, J. Crystal Growth 31 (1975) 223. [13] The literature on this topic is extensive; see. for example, the numerous papers in the two volumes Heteroepitaxy on Silicon. of the Materials Research Society Proceedings: Vol. 67. Eds. J.C.C. Fan and J.M. Poate (1986) and Vol. 91, Eds. J.C.C. Fan, J.M. Phillips and B.-Y. Tsaur (1987). [14] N. El-Mary, J.C.L. Tarn. T.P. Humphreys. N. Hamaguchi. N.H. Karam and S.M. Bedair. Appl. Phys. Letters 51 (1987) 1608. [IS] T.Y. Liu. H. Kroemer and Z. Liliental-Weber. unpublished. [la] J.W. Lee, H. Shichijo. H.L. Tsai and R.J. Matyi. Appl. Phys. Letters 50 (1987) 31. 1171 Y. Itoh. T. Nishioka, A. Yamamoto and M. Yamaguchi, Appl. Phys. Letters 52 (1988) 1617. [I81 E.A. Fitzgerald. P.D. Kirchner, R. Proano. .D. Petit. J.M. Woodall and D.G. Ast. Appl. Phys. Letters 52 (988) 1496.
330 Selected Works of Professor Herbert Kroemer ti. Kroemrr el 01. / G d s on si und relaled sxsrrms: prohlcvnr und pro.~pecr.$
102
G. Griffiths. K. Mohammed. S.Subbana. H. Kroemer and J.L. Merz. Appl. Phys. Letters 43 (1983) 1059. I201 J.S. Ahearn and P. Uppal. personal communication. .1211. T.Y. Liu. P.M. Petroff and H. Kroemer. to be published. 1221- L.C. Kimerling and J.R. Patel. in: VLSl Electronics. Vol. 12. Ed. N.G. Einspruch (Academic Press. Orlando. FL.. 1985) p. 223.
[23] K. Fischer. J. Klem. C.K. Peng. J.S. Gedymin and H. M o r k q . IEEE Electron Device Letters EDL-7 (19x6) I 12. [24] See. f o r example, H. Kroemer. J . Vacuum Sci. Technol. El (19x3) 126.
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H. Kroemer, C. Nguyen, and E. L. Hu, "Electronic Interactions at Superconductor-Semiconductor Interfaces," Solid State Electron., Vol. 37(4-6), pp. 1021-1025, 1994. Copyright 1994, with permission from Elsevier.
332 Selected Works of Professor Herbert Kroerner Solid-Siarc Elerrronrcs Vol 37. Nor 4-6. pp 1021-1025. 1994 Copyright h 1994 Elscvier Science Ltd pnnicd in Great Bntain All nghlr r c w r d OO38-I 101194 16 00 + 0 M)
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ELECTRONIC INTERACTIONS AT SUPERCONDUCTOR-SEMICONDUCTOR INTERFACES HERBERT KROEMER, CHANHNGWENand EVELYN L. HU Department of Electrical and Computer Engineering, University of Californ~a,Santa Barbara. CA 93106, U.S.A. Abstract-Two current flow mechanisms across a superconductor- mic conductor-superconduclor double
heterostructurc are discussed: the conventional proximity effect. and Andreev reflections. The emphasis is on Nb-InAs-Nb structures, with the InAs being in the form of a quantum well with AlSb barriers. for which current flow by multiple Andreev reflations can lead to an enhancement of the zero bias conductance by a large factor. For sufficiently short interslectrode spacings, the multiple Andreev reflections can lead to a m e supercurrent flow.
1. INTRODUmON
When a superconductor and a semiconductor are brought together into atomically intimate contact, with an interface that is free from intervening oxides and/or contaminants, and which does not form an electron-blocking Schottky barrier, the electrons in the two materials can interact with each other in ways that can drastically alter the current flow through what may be called “Super-semi-super double heterostructures”. An example of a particularly suitable structure for the observation of such interaction effects is shown in Fig. 1[1-3). It consists of a thin layer of InAs. in which the electrons are confined at top and bottom by AlSb barriers, forming a two-dimensional electron gas. This gas is then contacted by superconducting Nb electrodes. One of the reasons for the use of InAs is that the Fermi level at metal-InAs contacts tends to be pinned inside the lnAs conduction band, thus leading to an absence of Schottky barriers impeding the flow of electrons. As a result, such structures behave like pure resistors above the critical temperature of the Nb electrodes (9.2 K), and any new effects due to supersemi interactions are especially pronounced, unencumbered by non-superconducting complications. The reason for singling out a quantum well over a bulk structure is to achieve high electron concentrations by modulation doping while retaining high mobilities[4], and to suppress mobility reductions due to surface scattering, a problem especially severe with InAs, because of the absence of surface band bending. Typical sample parameters are: Well width of I5 nm, a channel length ranging from sub-pm dimensions to several pm, and an electron sheet concentration of several-times cm-’. The super-semi interaction effects in such structures are pronounced. Figure 2 shows the 4.2K differential conductance of a structure as in Fig. 1, as a function of bias voltage[3]. The device shows a very narrow conductance spike around zero bias, inside
which the conductance is enhanced by a factor 7 relative to the conductance just above the critical temperature of Nb (9.2 K). With increasing bias the conductance decreases. but shows a rich structure up to bias voltages equivalent to the superconducting gap of Nb ( z3.2 mV),These phenomena disappear when the Nb electrodes “go normal”. The structure and the behavior shown are by no means the only manifestation of super-semi interactions, nor are advanced quantum well structures necessary for all such observations. A variety of interaction phenomena have been observed in a variety of structures, employing a variety of semiconductors, including GaAs[5], (Ga,In)As[6], and Si[7]. Complete references can be found in the papers cited. 2. PROXIMITY EFFECT, WEAK LINKS AND
JOSEPHSON FETs
There are two distinct basic forms of super-semi interactions: the well-known Proximity Effect, and the less-well-known, but perhaps more important Andreev Refections. In the conventional proximity effect, the Cooper pairs that are the carriers of supercurrent inside the superconductor, can tunnel into the a normal conductor, causing induced superconductivity there, falling off exponentially with distance, with a characteristic length called the coherence length. If the separation between the superconducting electrodes is sufficiently small-typically of sub-pm dimensionsthis can lead to what is called a wenk link. a structure capable of carrying a true resistance-less supercurrent through the semiconductor. In 1980, Clark er a1.[8] drew attention to the promise of semiconductors rather than conventional metals as the non-superconductor in proximity effect studies. They proposed a Hybrid Josephson FET ( = JOFET), basically a weak link the critical current of which can be modulated, leading to a current-voltage characteristic resembling that of a field
1021
Reprinted Articles 333 HERBERTKROEMER et a/.
1022
t
t
7
t
Gate
Source
7 Drain
t I
Electrons & Current Fig. I. Schematic InAs-AISb quantum well structure with superconducting Nb electrodes. for the investigation of electron-elcctron interaction effects across a super-semi interface.
effect transistor, except for a very different voltage scale, in the low-mV range, and of course a very different physics. The central idea was that the critical current that can be passed through a weak link employing the proximity effect depends strongly on the superconductive coherence length inside the semiconductor, which in turn depends o n the electron concentration in the semiconductor, which can be modulated with a gate electrode. The overall result would be a current-voltage characteristic as shown schematically in Fig. 3. What distinguishes JOFETs from conventional FETs are not only the much lower voltage (and current) scales. but the existence of a true zero-resistance on-state. This makes a JOFET a device of potential interest as a current routing switch in superconducting networks. There is some doubt as to whether such JOFETs would ultimately be useful as
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-
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4.0
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T = 4.2 K
3.0 2.0 1.o
0.0
t
Drain current Increasing positive gate voltage
Drain voltage Fig. 3. Schematic JOFET structure and its I-V characteristics.
amplifiers or logic gates: the gate voltage swings required for current modulation tend to be larger than the drain voltage swings obtainable from the current modulation. Clark er nl. pointed out that InAs appeared to be the ideal semiconductor for such studies, not only because of the absence of Schottky barriers at metalto-InAs interfaces, but also because of its unusually high electron mobilities. which in turn reflect the low effective mass of electrons in InAs. Because of this low effective mass, heavily n-type doped lnAs has a Fermi velocity approaching that of many true metals, and as a result, lnAs in contact with a superconductor behaves more like a high-mobility metal than like a semiconductor. In particular, large coherence lengths should be achievable. Weak links and JOFETs employing a N b l n A s N b structure were subsequently demonstrated, by Takayanagi er aL[9,lO], followed by others. However. the current-voltage characteristics of those early structures were relatively poor, and JOFETs with much better characteristics were obtained in GaAs and even Si[7], despite the theoretical superiority of InAs. Perhaps the most interesting of those early JOFET structures was that of lvanov er al.[5],which appears to have been the first l o employ a quantum well channel [GaAs-(AI,Ga)As] in a weak link or JOFET, demonstrating the superiority of such a design.
1 0.0 1.0 2.0 3.0
-3.0 -2.0 -1.0
V[mVI Fig. 2. Very strong enhancement at zero bias of the differential conductance of a recent InAs-AISb quantum well struaure with Nb electrodes[3]. of the type shown in Fig. 1, with a I pm electrode separation. The rich structure shown on the Banks of the central identifies the conductana peak ar due to multipk Andreev reflections (see text).
334
Selected Works of Professor Herbert Kroemer Interactions at supersemi interfaces Following the development of a technology for high-quality InAs-AISb quantum wells during the 1980s. we ourselves turned to the problem of InAs weak links, and the balance of this paper deals with that work. In 1990 we were able to demonstrate weak links showing unprcccdentedly high critical current densities above 2 x lo5A/cm*, for a remarkable large inter-electrode spacings of 0.6 pm[l]. We were naturally interpreting these results as caused by the conventional proximity effect. More recent observations challenge this interpretation, and suggest a different superconductivity mechanism in terms of multiple Andreev Reflections. our next topic.
1023
+m
...r -
.........
...
............ .^ ........... -..... ...............*.
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5. Multiple Andreev reflections (AR) alternating between the super-semi interfaas at opposite ends of the
3. ANDREEV REFLECnONS
semiconductor region.
Consider a semisuper interface between a degenerately doped semiconductor and a superconductor, with a band diagram as shown in Fig. 4. On the superconductor side, a superconducting energy gap has opened up. If now a small bias voltage V is applied, as shown, the existence of the gap then prevents a single electron at the Fermi level of the semiconductor from entering the superconductor. This argument suggests that, in the absence of the proximity effect, the onset of superconductivity in the metal thus actually increases the electrical resistance to current flow across the interface, due to this gap formation. However, even a single electron may pair up with a second electron at the bias energy qVbelow the Fermi level, forming a Cooper pair, which can enter the superconductor, causing a doubling of the current compared to that in the absence of superconductivity, rather than the reduction that would occur in the absence of this pair formation. As the electron below the Fermi level is removed from the semiconductor, it leaves behind a hole below the surface of the Fermi sea. The generally accepted jargon associated with this phenomenon is to say that the incident electron is rejected us a hole, a kind of reflection process called an Andreev reperfion, honoring the originator of the concept[l I]. The Andreev hole left behind, being a “bubble” under the surface of the
Level
.........
.”........--._.........
... .... .._....... I.”
Andreev Hole
Fig. 4. Andreev reflection (AR) of an electron at a biased super-semi interface.
Fermi sea in the conduction band, must not be confused with a valence band hole. In a semiconductor with a large mean free path for 3 in our structures), the Andreev the electrons ( ~ pm hole left behind at the interface has a large mean free path itself, roughly equal to that of the electrons, and theory shows that the hole travels back into the semiconductor along a trajectory that is essentially the time reversal of the trajectory of the original incident electron. If its mean free path is sufficiently large, the hole will eventually reach the negative superconducting electrode. If the bias across the structure is sufficiently small. the energy of the hole is still within the superconducting gap on that side. Such a hole cannot enter the superconductor, but it can be annihilated by breaking up a Cooper pair inside the adjacent superconductor: one of the electrons of the pair annihilates the hole, the other electron takes up the annihilation energy, and is injected into the semiconductor as a ballistic electron above the Fermi level, at an energy above that of the initial electron. This process. illustrated in Fig. 5 , can evidently be repeated, until either an electron or a hole has been “pumped up” to an energy outside the superconducting gap, on one of the two sides of the structure. If all reflections of electrons and holes were Andreev reflections rather than “ordinary” reflections, the result would be an enhancement of the conductivity by a factor equal to the number of ballistic round trips before escape or before collision events randomize either the electron or the hole flow in this chain reaction. As a rule, the conductance enhancement in past structures has been much smaller, presumably due to a low AR probability, itself caused by strong normal reflections due to residual potential barriers at the interfaces. One of the “fingerprints” of multiple ARs is a rich “sub-harmonic gap structure” in the conductance-vsvoltage characteristic, with steps occurring at voltages equal to the integer fractions of the superconducting gap voltage[l2-14]. A discussion of this structure lies outside the scope of the present paper,
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HERBERTKROEMER et ol.
but the Occurrence of such I structure is evident in the characteristics of Fig. 2, thus clearly indicating the multiple-AR origin of the conductance peak. What is new compared to earlier data reported in the literature is the huge enhancement in the differential conductance. by a factor of 7 in the example of Fig. 2. The behavior appear superficially as if the proximity effect were present. However, we will show below that contact resistance measurements rule out such an explanation. 4. ANDREEV-REFLECTION-INDUCED SUPERCONDUCI’IVITV
The large conductance enhancement suggests that it might be instructive to carry the above multiple-AR argument to its extreme limit, the case of zero applied bias, and assuming that all reflection events at the super-semi interfaces are AR events, and that no scattering of any kind inside the semiconductor randomizes the electron and hole velocities. In this case, a given AR “chain” would go on forever. During each electron-hole round trip, one Cooper pair is annihilated at one of the electrodes, and re-constituted at the other electrode on the opposite side, leading to the net transfer of one Cooper pair per round trip. Given an initial net current, this current would persist, just as in the proximity effect, but by an altogether different mechanism. These are extreme assumptions, especially the assumption of a 100% AR probability, yet the final conclusion appears to be correct. The quantum mechanics of this hypothetical multiple-AR mechanism has recently been analyzed in detail by Schiissler and Kummel (SK)[IS], using a model assuming the existence of a definire fixed phase difference between the pair potentials in the two superconducting electrodes. and neglecting scattering in the semiconductor channel, but not assuming a 100% AR probability. The authors showed that under their conditions the multiple Andreev Reflections of phase-conjugate ballistic quasi-particles (i.e. electrons and Andreev holes) form indeed a very effective mechanism for Cooper pair transfer between the electrodes. capable of carrying a much higher zero-resistance current densities than the conventional proximity effect. We believe that the narrow central conductance spike shown in Fig. 2, with the up-to-sevenfold enhancement of the differential conductance, is a precursor of the true Andreev-caused supercurrent postulated above. and analyzed by SK. We have to call it a precursor, because our data indicate a still-finite conductance, occurring over a narrow but nonzero voltage range ( 9 50 p V). Presumably. the finite height and width of the central conductance spike is the result of residual scattering events present in the relatively long ( I p m ) InAs-AISb QW channel. eventually randomizing the quasiparticle velocities. Furthermore, we belicve that the true superconducting limit can indeed be achieved in Nb-lnAs-Nb
quantum well structures with a shorter inter-electrode spacing. In their work. SK mmmp that there is a fixed phase relation between the pair wave functions in the two superconducting electrodes. and analyze the consequences. They do not address the question of how such a phase relation. and with it any supercurrent. might be maintained in the presence of scattering in the semiconductor channel. In the absence of such scattering. the assumption of a fixed phase relation between the pair wave functions in the two superconducting electrodes is entirely self-consistent. On the other hand. in the presence of sufficiently strong scattering. as in the case or a sufficiently wide interelectrode spacing, any current not driven by an external voltage must eventually decay. This raises the question as to the nature of the transition to the SK superconducting limit, as the scattering in the semiconductor channel is reduced, by reducing the temperature and/or the inter-electrode spacing: will the zero-bias resistance of the overall structure drop towards zero continuously, without ever reaching the true superconducting limit? Or will collective effects cause a “condensation” of the Andreev pairs into a new correlated many-body state, in which the dephasing effects of scattering are quenched. similar to the way the BCS transition quenches the ordinary resistivity in a BCS superconductor? We believe that the latter is indeed the case. and that our earlier observation of very large wcak link current densities in structures with 0.6 p m electrode spacing was indeed a manifestation of such a mechanism. To pursue this idea further. we have utilized laser holography to prepare what is essentially a grating of 4 300 parallel Nb lines making periodic contact to an lnAs quantum well with AlSb barriers. with a I p m period and a - 0 . 4 p m spacing between the Nb lines. The rest of the technology was basically the same as in the structure whose data were shown in Fig. 2. In the direction perpendicular to the grating lines. the structure acts basically as a series-connection of 300 diodes of the type shown in Fig. I . At 4.2 K. this structure showed a characteristic qualitatively similar to that of Fig. 2. with the “Andreev fingerprint’‘ of sub-gap harmonics. but with a -300-fold enhanced voltage scale. More importantly. the conductance enhancement was by a factor 75. presumably as a result of the shorter inter-electrode spacing. With decreasing tcmpcrature. the zero-bias resistance dropped further. reaching an immeasurably low value between 3.9 and 3.8 K. This grating structure was still being evaluated at the time of the deadline for this manuscript: up-todate results will be presented at the conference. 5. THE CONTACT RESISTANCE PROBLEM
Our interpretation of the conductance enhancement in terms of multiple ARs rather than as a precursor of the ordinary proximity effect is sup-
335
336 Selected Works of Professor Herbert Kroemer
*
Interactions at super-semi interfaces
1025
Cooper pairs. We would then expect the true contact
y = 0.048272 + 0.017904~R= 1
2*oo
resistance associated with the Nb-InAs interface to be zero, and the resistive portion of the semiconductor path to be shortened below the lithographic length, leading to a negariue value of the intercept voltage ZV, and to a negative apparent contact resistance, represented by the leading term in eqn (1). Our measurements, shown in Fig. 6, indicate that the apparent contact resistance remains positive, thus ruling out the proximity effect as an explanation of the zero-bias conductance spike.
Acknowledgements-This work was supported in part by the Office of Naval Research and in part by the National Science Foundation. the latter through the NSF Science and Technology Center for Quantized Electronic Structures, grant no. DMR 91-20007. as well as through the NSF ' ) " ' " ' ' " ' ~ " " 0 20 40 60 80 100 Materials Research Laboratory Program, Award no. DMR 912-3048. One of us (C.N.) wishes to acknowledge the financial support from the UCSB Vice Chancellor's FellowLIPml Fig. 6. Zero-bias diEercntial resistance R = d V/dl at 4.2 K ship for Advanced Research on Quantized Structures. of a set of Nb-InAs(QWpNb swucturcs with dicerent inter-electrode spacings, plotted as function of spacing. The straight line is a linear fit through the data, including a point at L = 200 pm. not shown on the plot. T h e intercept value, REFERENCES representing twice the line contact resistance, is positive.
ported by measurements of the specific contact resistance at the Nb-InAs interface, using the conventional transmission line method widely used in semiconductor technology[l6]. The latter consists of measuring the set of voltage drops across a monolithic array of metal contacts to a thin semiconductor layer, with various lithographic intercontact spacings L, and fitting the measured voltages and their current derivatives to an expression of the form: dV
-dl=
dV, dl
2-+p;-.
L W
Here i i s the current through the array, w is the width of the array, and pr is the ordinary sheet resistance of the semiconductor layer in the limit that L and H' are large compared to the electron mean free path. In cqn (l), the length-proportional term represents the "ordinary" path resistance of a semiconductor path of length L, and 2dVJdl represents the effects of whatever additional voltage drops are present at or near the two contacts. The latter include the true contact resistances at the two interfaces, plus any deviations from bulk behavior inside the semiconductor near the electrodes, for example due any proximity effect. If the latter is present, a d.c. current across the super-semi interface would be carried entirely by
I . C. Nguyen. J. Werking. H. Kroemer and E. L. Hu, Appl. Phys. Leu. 57, 87 (1990). 2. C. Nguyen, H. Kroemer and E. L. Hu, Ph.vs. Rw. Leu. 69. 2847 (1992). 3. C. Nguyen. H. Kroemer and E. L. Hu, to be published. 4. C. Nguyen, B. Brar. C. B. Bolognesi, J. J. Pekarik. H. Kroemer and J. H. English, J . Elecrron. M a w . 22. 255 (1993). 5. 2.Ivanov, T. Claeson and T. Anderson. Japan. J . appl. Phys. 26(Suppl. 3). DP31 (1987). (Proc. 18th Int. Conf. Low Temperature Physics, Kyoto, 1987). 6. A. Kastalsky. A. W. Kleinasser. L. H. Greene. R. Bhat, F. P. Milliken and J. P. Harbison, Phys. Rw. Lptr. 67, 1326 (1991). 7. T. Nishino. M. Hatano. H. Hasegawa, F. Murai, T. Kure, A. Hiraiwa, K. Yagi and U . Kawabe. IEEE Electron. Deoirc. Lerr. 10, 61 (1989). 8. T. D. Clark, R. J. Prance and A. D.C. Grassie J . appl. Phvs. 51, 2736 (1980). 9. H. Takayanagi and T. Kawakami, Phys. Rev. Leu. 54, 2449 (1985). 10. H. Takayanagi and T. Kawakami, Proc. In/. E(Pcrron Dwices Meering, p. 98 (1985). I I . A. F. Andreev. So?. Phys. JEPT 19. 1228 (1964). 12. T. M . Klapwijk, G. E. Blonder and M. Tinkham. Ph.vsica E + C 109 & 110, 1657 (1982). 13. M. Ocfavio, M. Tinkham. G. E. Blonder and 7.M. Klapwijk. P h w . Rec. B 27, 6739 (1983). 14. K. Flensberg, J. B. Hansen and M. Octavio, fhys. Rw. 8 38. 8707 (1988). IS. U. Schiissler and R. Kiimmel. Phys. Rev. B 47, 2754 ( 1993). 16. R. E. Williams. Gullium Arsenide Processing Techniques. Artech House. Dedham, Mass. (1984).
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1 did not intend to invent compact disc players." Herbert Kroemer
Reprinted with permission from
H. Kroemer, Superconductor-Semiconductor Devices," NATO Adv. Res. Workshop Future Trends in Microelectronics: Reflections on the Road to Nanotechnology, Ile de Bendor, France, S. Luryi, J. Xu, and A. Zaslavsky, Eds., NATO AS1 Series; Series E: Applied Sciences, Vol. 323, Kluwer Academic Publishers, pp. 237-250,1996. "
With kind permission of Springer Science and Business Media.
338 Selected Works of Professor Herbert Kroerner
SUPERCONDUCTOR-SEMICONDUCTORDEVICES HERBERT KROEMER ECE Department, University of California Santa Barbara, CA 93106, USA
1. Introduction 1.1
THEPREMISE
It has long been recognized that electronic devices operating at reduced tempraturesincluding both semiconductor and superconductor devices-an often offer much higher performance (by several criteria) than room-temperature devices. But the need for cooling has greatly retarded their use, and there exists an almost-universal persistent belief that low-temperature devices just don’t have a chance to find significant practical applications. My presentation is based on the premise that this belief is a myth, and that the future of electronics is likely to draw increasingly, within the next decade or two, on low-temperature devices, at least in applications such as high-performance workstations and scientific and medical instrumentation, where increasing performance requirements can justify the additional cost of the cryogenics, which is itself decreasing However, the performance-to-cost relation is by no means the only issue: No matter how favorable that relation is, no system engineer is going to fool around in a “real” commercial system with cryogenics under conditions that resemble those of a research laboratory. What is absolutely essential is “user-friendly” cryogenics! The enabling technology for the widespread actual use of cryogenic electronics is likely to be the increasing availability of small self-contained closed-cycle refrigerators. The development of the latter (mainly Stirling-cycle machines), originally driven by IR detector technology, has more recently found increasing use in high-T, superconductor applications. It is rapidly approaching the point that we may begin to view such a refrigerator as just another module inside a piece of electronic equipment, somewhat analogous to, say, a fancy high-voltage power supply. 237 S. h r y l et al. (ea!s), Future Trends In Microclectronlcs, 237-250. 0 1996 Kluwcr Acdemlc Publishers. Printed in the Nettherlands.
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238 Suppose I offered you a self-contained box, about 2-3 liters in volume, drawin less than 100 Watts, and I would provide inside this box a volume of about lOOcm inside which I guarantee a temperature T,of say, 77K,with a cooling capacity of, say 3-4 Watts. Given a reasonable cost, such a box would evidently meet our demand for user-friendly cryogenics. The above specifications are not fictitious, they are those of actual hardware about to go into production, interestingly by a company whose business is in the field of high-T, superconductors, and which has found it necessary to provide integrated system solution to its customers, solutions that include a usertransparent cryogenics package (SuperconductorTechnologies, Santa Barbara,CA). The principal bottleneck to their more widespread use is their cost, but this is likely to follow the classical pattern of dramatic cost reduction in the wake of building up mass production. Furthermore, the specifications are likely to improve with time, including rapid progress to lower temperatures with time, at least to about 20K, the practical limit of the Stirling cycle, with slower progress below that.
f
1.2.
SUPERCONDUCTOR-SEMICONDUCTORDEVICES
I .2.1. Hybrids With Buffer Layers The devices that very likely will emerge in the wake of this development will not only be supemohducting devices using high-T, superconductors, and conventional devices such as FET’s explicitly designed to operate at low temperatures, but also integrated super-semi hybrids. The first class likely to emerge are high-T, superconductors integrated on-chip with semiconductordevices, like a superconducting SQUID integrated with GaAs or InAs electronics. Because of processing compatibility limitations, such devices require a buffer layer between the two kinds of materials, a technology in which much progress has been made recently [l, 21. But, being devices operating at temperatures within easy range of the Stirling cycle, such devices should emerge relatively soon.
1-2.2. Monolithic Integration without Inredace Barrier As “practical” temperatures get pushed lower, we will also see devices in which a lowT, superconductor,such as Nb,has been integrated with a semiconductor, such as I d s , without an intervening layer, in such a way that the electrons can cross the interface while retaining the phase information that is the essence of superconductivity,thereby inducing superconductivity in the semiconductor, New kinds of Josephson devices based on this principle are rapidly emerging, offering advantages over more conventional Josephson devices. In fact, much of my presentation-all of Section 2will deal with this particular combination, as a look far ahead at a branch of lowtemperature transport physics that is likely to become important over the long term.
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239 For the near-term future (< 10 years), the need for operating temperatures below the Stirling-cooler range (< 20K) implies more elaborate cryogenic techniques, and these devices may, for some time, remain restricted to two kinds of applications environments: (a) Environment where cryogenic temperatures are available in any event, and where cryogenic electronics can be piggy-backed on the existing cryogenics with minimal additional cost. (b) Large-scale “ultimate-performance” computer mainframes the cost of a helium liquefier would represent only a small fraction of the cost of the overall machine. 1.3.
ON NOT REPEATING THE PAST
Anybody invoking this last scenario as a realistic one for the future must address himor herself to the fact that a huge effort of precisely this kind was undertaken by IBM during the 70-s, only to be abandoned in 1983. The failure of this project had a terribly discouraging effect on the whole field of low-temperature electronics, and anybody reconsidering this approach is in danger of running afoul of Santayana’s famous dictum that “those who do not remember the past are condemned to repeat it.” It has been argued persuasively by Likharev [3] that this failure was due, not to the need for liquid-helium temperatures, but to two quite unrelated reasons: (a) The use of a unsuitable aon-refractory metallurgy based on lead as a superconductor, which was not sufficiently stable under thermal cycling. The resulting reliability problems would have been avoided by using niobium as a superconductor. (b) The use of a logic principle, employing voltage-state logic, that was basically too imitative of semiconductor logic, and which had inherent power dissipation limits that negated much of the speed advantage of Josephson junctions. As Likharev points out, a much more suitable form of superconducting logic would be one that is based on the unique property of superconductors that magnetic flux in superconducting loops is quantized, and which shuffles single flux quanta rather than shuffling voltage states. Likharev’s own presentation at this workshop reviews the present state It would constitute a major breakthrough for superconductor-semiconductor devices if a high-temperature superconductor could be found that is technologically compatible with existing semiconductors,especially Ill-V semiconductors. As it stands now, all the high-T, superconductors are oxides that must either be deposited, or require a post-deposit anneal, in a high-temperature oxidizing atmosphere that will simply destroy any of the semiconductors it is in atomic contact with, thereby eliminating barrier-free structures. Current research on high-T, superconductors stresses the achievement of higher critical temperature, rather than elimination of the need for a high-temperature oxidizing environment. From the point of view of super-semi devices, the achievement of semiconductor-compatiblematerials would be a far more valuable goal, even if it meant a drastic reduction in critical temperature, say, to 40K.
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2. Semiconductor-Coupled Superconducting Weak Links 2.1,
INTRODUCTION
As the title of my presentation indicates, its objective is restricted to low-temperature devices in which superconductors and semiconductors are rnonolithically integrated into a common device, ignoring both “pure” superconductor devices-such as Josephson tunnel junctions-that do not involve a semiconductor, and pure semiconductor devices that just happen to be specifically designed for low-temperature use. In fact, my presentation concentrates on what I consider the potentially most interesting form of monolithic superconductor-semiconductor integration, namely, semiconductor-coupled superconducting weak links. Much of contents of this section is based on a recent longer introductory review of this topic by Professor Hu and myself (41, where the interested reader may find additional details and additional references. An earlier elementary introductions is found in [5]. The term weak links refers to superconducting devices in which two superconducting “banks” are coupled through another conducting medium, as opposed to Josephson tunnel junctions, in which the current flow is by Cooper pair tunneling through an insulating barrier. In the case of interest here, the conducting medium is a semiconductor rather than a metal. More specifically, it is a narrow (-15nm) InAs quantum well with AlSb barriers, fonning a short (elpm) conducting link between two Nb superconducting banks, schematically shown in Figure 1. For reasons I will discuss below,this combination has emerged as a particularly promising one.
t k - 9 I
lnAs
t 1
......................... 110-15 .........................nm
t
Figure 1. Semiconductorcoupledsuperconducting weak link based on an InAs-AISb quantum well forming a conducting link between two superconducting Nb electrodes.
Like Josephson tunnel junctions, weak links exhibit a pronounced Josephson eflect, manifested by a current-voltage characteristic as in Figure 2, which shows data from a semiconductor-coupled weak link of the kind shown in Figure 1. The characteristic feature of the Josephson effect is the existence of a current range inside which a resistance-less supercurrent can flow between the two superconductingbanks, up to a
342 Selected Works of Professor Herbert Kroemer
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certain critical current I,. Only when this current is exceeded does a voltage appear between the superconducting terminals. Compared to tunnel junctions, weak links have a much larger inter-electrode separation between the two superconducting banks, which leads two potential major advantages: (a) much lower capacitances, an important consideration for the use of these devices as high-speed devices (b) a much smaller sensitivity of the characteristics to variations in the electrode separation.
2.0
I
,
,
,
.
1
.
-2.9 K 1.o
T- 0.0 a
-
"
'
1
3.9 K
_---- .
L = 0.6pm b = 50pm
L
,
4
I
-
-1 .o
-2.0 -2.0
'
-1.o
0.0 v [mVI
1.o
-
Figure 2. Josephson-typeI-V characteristics of a device as shown in Figure 1, with 0.6pm electrode separation. at two temperatures [6].
I will not address myself here to the actual applications of semiconductor-coupled weak links. In principle, weak links are candidates for all applications for which Josephson tunnel junctions are candidates, with the advantage of higher potential speed, and a technology that lends itself naturally to integration with semiconductor circuitry, including monolithic integration in which the latter operates at the temperature of the weak link itself. One specific application is of course in computers based on the Josephson effect, a topic where I gladly defer to Likharev's presentation at this workshop. However, as I have stated in my earlier presentation at this workshop, the principal' applications of any sufficiently new technology tend to be applications created by the new technology-which at this time must be left open to speculation.
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BASIC WEAK LINK PHYSICS: A TUTORIAL
Current-Phase and Phase- Voltage Relations An understanding of weak links requires at least a rudimentary understanding of the basic physics underlying Josephson junctions in general, and weak links in particular. I summarize her the basic facts, without justifications or derivations, for which I must refer to relevant texts (see, for example, refs. [7-101). 2.2. I .
The Pair Wave Function and its Phase. The essence of superconductivity is the existence of a common pair wave function for the Cooper pairs in the superconductor, which may be written
Here, the magnitude Iy(r)lof the pair wave function is related to the local Cooper pair density n(r) via
and 8 (r) is a phase. The key point is that this phase is coherent over macroscopic distances, and, in the absence of a current, it is the same throughout the entire superconductor.
Supercurrent as a Function of the Phase Difference. In a weak link, two superconductors are coupled through another conducting medium, through which electrons can pass in such a way that the phase of the electrons is preserved in the process. If the phases of the two superconductors are the same, there will be zero net current, but if there is a phase difference between the two superconductors, a resistanceless Josephson supercurrent can flow from one superconductor to the other, the magnitude of which is a function of the phase difference 4 81 For Josephson tunnel junctions the functional relationship is simply sinusoidal,
-
Here, with the ordering of the two phases as given, a positive current designates a flow of Cooper pairs from bank #2 to bank #1. Because the pairs carry a negative charge -2e, the electrical current is in the opposite direction, from bank #1 to bank #2. In weak links, more complicated relations may occur, but Z(% - 0,) is always an odd function
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of the phase difference, and inasmuch as phase differences have a physical meaning only modulo 2x, the I(%- 6,) relation is necessarily a periodic one, with a period 2x.
In the absence of a bias voltage between the two superconducting banks, whatever phase difference % - 6, may be present, will not change with time, hence the current will continue to flow-which is why it is called a supercurrent. If an external bias voltage is present, the difference becomes time-dependent according to the simple law
A.C. Josephson Efect.
-(62 d
-e,)=--.(v, 2e -v, ).
dt
A
(4)
-
The supercurrent-vs.-phase relation I(% 6 , ) remains valid in the presence of such a voltage, but the supercurrent now oscillates about zero, with the Josephson frequency
where h = 2xh is Planck’s constant. 2.3. 2.3.1.
ANDFtEEV REFLECTIONS
Semiconductor-Coupled Weak Links as “Clean Weak Links The weak-link physics of Sec. 2.2 holds independently of the nature of the mechanism that preserves the phase of the electrons, In the semiconductor-coupled weak links discussed here, the mean free path of the electrons tends to be larger than the interelectrode separation, in which case the mechanism for the phase transfer tends to be dominated by the phase-coherent flow of ballistic electrons between the banks. In the jargon of superconductivity,such weak links are called “clean” weak links, in contrast to the more common “dirty” weak links extensively studied in the past, in which the electron transport is diffusive. Unfortunately, much of the literature on weak links, including Likharev’s classical review of weak links [ 111, is still dominated by considerations of dirty weak links. The mean free path that matters for the phase transfer is not the elastic mean free path that determines the low-field mobility, but the inelastic mean free path that is responsible for any de-phasing of the electron waves, and which is typically much longer than the elastic mean free path. For example, in impurity scattering the phase of the scattered wave is coherent with the phase of the incident wave, and while such scattering may create a chaotic wave front, this does not constitute phase-incoherence It
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in the sense of weak link theory: there is still a fixed phase relation between any two points in the wave field. Given an inelastic mean free path much longer that the inter-electrode spacing, the dominant phase-altering process for the electrons becomes the scattering, not inside the semiconductor, but at the semiconductor-superconductor interface, between the electrons in the semiconductor and those in the superconductor. Now, electron-electron scattering is normally a phasedestroying process. However, at a super-semi interface, at sufficiently low temperatures, the only electrons available for participation in scattering on the superconductor side are the Cooper pairs. But, as we saw earlier, the Cooper pairs all have the same well-defined phase. As a result, the scattering interaction of electrons in the semiconductor with electrons in the superconductor becomes itself a phase-coherent process. It is universally referred to as Andreev scattering or, more commonly, as Andreev reftecrions (AR's), in honor of the man who discovered the possibility of such a process in 1964 [ 121. Although postulated over thirty years ago, Andreev reflections have received major attention only during the last few years, when it became clear that their understanding is central to the understanding of clean-limit weak links. As a result of this belated recognition, they have not yet found their way into current textbooks on superconductivity. Even the 1979 weak-ink review by Likharev, written just before clean weak links became technologically realizable, mentions Andreev reflections only in passing. In fact, on page 132 of his paper (1 11, Likharev explicitly lists a number of experimental observations that are not consistent with the then-existing theoretical understanding, all of which find their explanation via Andreev scattering. I therefore provide here the necessary background on this topic.
2.3.2. Andreev Refections: Basic Concept The basic idea behind Andreev reflections is simple. Consider an interface between a degenerately doped semiconductor and a superconductor. As shown in Figure 3a, a superconducting energy gap has opened up on the superconductor side. If now an electron with an energy & above the Fermi level (but still inside this gap) is incident on the interface from the semiconductor side, the absence of single-particle states within the gap prevents that electron from entering the superconductor as a single electron, and one might expect this electron to be reflected, and the electrical resistance to current flow across the interface actually to increase at the onset of superconductivity in the metal. However, the electron may pair up with a second electron at the same energy & below the F e d level, forming a Cooper pair, which can enter the superconductor, causing a doubling of the current compared to that in the absence of superconductivity, rather than a suppression. The electron removed from the semiconductor below the Femi level leaves behind a hole in the Fermi sea. The generally accepted jargon
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picture of Figure-3b, and must take into account the wave properties of the unpaired electrons arld holes, andbf the Cooper p&s [ 131. 2.3.3. Andreev Supercurrents Waves have phase, and even in the absence of any scattering events, the simple currentcarrying state illustrated schematically by Figure 3b is a quantum-mechanically allowed stationary state only if the round-trip phase shift along the electron-hole loop is an integer multiple of 2x,
For every value of n, there will actually be two states, corresponding to opposite directions of the flow mows in Figure 3b. Up to a point, the above is exactly the same condition as for the bound states in an “ordinary” one-dimensional semiconductor quantum well. These, too, are states for which the round-trip phase changes are the different multiples of 2x. In fact, with regard to the spatial confinement of the unpaired electrons and holes inside the semiconductor portion of the structure, the stationary states may indeed be viewed as a new kind of bound states [13], the difference being that the “heterojunction” bamers are now formed, not by the conventional energy gap of another semiconductor, but by the superconductingenergy gap of the two superconductingelectrodes. However, there are two decisive differences. The first is that €or an AR state confined by superconducting energy gap barriers, the phase on one of the two traverses is carried by an electron, on the other traverse by a hole. This means that these kinds of bound states actually carry a current across the semiconductor, in contrast to the current-less conventional bound states in a conventional quantum well. The two states belonging to a given n belong to opposite directions of that current flow. A second difference is the following. As in a conventional quantum well with barriers of finite height, the round-trip phase shift contains a contribution from the reflections at the two superconductor barriers. In a semiconductor quantum well, these contributions simply represent the finite penetration of the wave function into the barrier, and they are respbnsible for lowering the bound state energies with decreasing barrier height. But in the case of Andreev reflections there is an additional phase shift at each bank, equal in magnitude to the phase of Cooper pair wave function in that bank, but with a sign dependin8 on whether an electron or a hole is reflected: When an electron is reflected at a superconductorwith phase 8, the wave function of the hole resulting from the reflection acquires an additional phase shift by -8. This can be readily understood by realizing that the Andreev reflection of an incident electron creates an additional
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Cooper pair with phase 8. The phase shift -8 of the reflected hole simply compensates for the phase of the new Cooper pair. Conversely, if a hole is reflected, the wave function of the resulting electron acquires the phase +8, with a similar interpretation. What matters for the Andreev bound states is of course the net round-trip phase shift. If the two superconducting banks have the same phase, the phase shifts by k0 at the two banks cancel, but if there is a phase difference between the two banks, it will make a contribution
to the round-trip phase shift, with the following sign rule: If, in Figure 3b, the left-hand bank is bank #l, the minus-sign applies, otherwise the plus sign. In order to retain the round-trip condition (6) in the presence of the phase shift contribution A@, the latter must be compensated for by an opposite change in the phase shift contribution associated with the ballistic flight through the semiconductor itself. But this leads to a change of the energy of the Andreev bound states: A positive contribution to the round-trip phase shift requires a lowering of the ballistic phase contribution, and hence a lowering of the bound-state energy, while a negative contribution raises the latter. Because of the sign difference in (7), in the presence of a nonzero phase difference 0, - 01, the energies of the bound states will depend on the direction of current flow in each state, in such a way that the states with a current flow in the direction proper for a Josephson supercurrent will have a lower energy and hence a higher thermal occupation probability, than those with a current flow in the opposite direction. Hence, in this case there will be a thermodynamically stable net current flow, even in the presence of scattering events. Recall finally that a time-independent phase difference corresponds to zero bias voltage. Hence the stable current is a true zero-resistance supercurrent, with a certain maximum value, the critical current, for some particular value of the phase difference
e, - 4When the current through the device exceeds the critical current, a bias voltage develops across the semiconductor, leading to the bending-over of the I-V characteristic seen in Figure 2. This dissipative regime contains itself a rich variety of physical phenomena, the discussion of which would again go beyond the scope of this paper; the interested reader is referred to the literature, probably starting with a few existing elementary review papers [4-61, which contain extensive references to key original papers, including specifically to papers on the detailed theory for the various phenomena.
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certificate that says, in effect: “This individual has proven that hehhe is capable to perform independent high-quality engineering or scientific work, has adaptability to a wide range of needs, and the ability to make, within a broad strategic context, the decisions about how to conduct that work.” This is far more useful than, say: “This individual has spent over four years studying the low-temperature optical absorption of sowhatnium, has honed the technique involved to perfection, and knows more about this specific topic than anyone else in the world.”
4. References 1. Lepselter, M. (1974) Integrated Circuits-The New Steel, IEDM Digest.
2. Kroemer. H. (1982) Heterostrudure Bipolar Transistors and Integrated Circuits. Proc. IEEE 70, 13-25. 3. Kroemer, H.(1%3) A Roposed Class of Heterojunction Lasers, Proc. IEEE 51, 1782-1783. 4. Kroemer. H. (1967) Solid State Radiation Emitters, U.S.Patent 3,309.553.
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350 Selected Works of Professor Herbert Kroemer 249
However, work on true (three-terminal) JOFET's forms only a small fraction of the overall recent work on semiconductor-coupled weak links that was stimulated by the original JOFET proposal. None of the JOFETs actually reported to-date have shown the kind of performance that offers promise for practical applications. One of their most severe problems is that the obtainable drain-to-source voltage swings are typically much less (> ImV) required to achieve significant drain current changes. These devices therefore have painfully low voltage gains, which appear to be inherent in their physics. Even the recent NTT devices just barely achieve a voltage gain of unity under optimal loading conditions. It remains to be seen whether or not future developments will overcome this problem. As it stands now, a more likely application of JOFETs is as current-routing switches in superconducting networks, drawing on the fact that a JOFET is an FET with a true zero-resistance onstate, something no pure semiconductor device can offer. 2.4.2 Multi-GapGrating Structures We ourselves have found it useful to go beyond a single-gap device geometry of Figure 1. and to study series-connected periodic arrays, prepared by laser holography, involving a large number (2 300) of gaps, shown schematically in Figure 4.
InAs
Figure 4. Overall layout (bottom)of Nb grating structufe. along with (top) a schematic cross-section through a pair of Nb lines separated by a narrow stripe of InAs-AISb quantum well. All dimensions ~ u in e pm.
We consider such grating structures particularly promising for future applications, and extensive studies of such structures are currently underway, to be reported in due course. Initial results are found in [a] and [4].
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References L. D.. Tseng, M. Z.,Fork, D. K., Young, K. H..and Hu,E. L. (1992) Epitaxial MgO buffer layer for YBa2Cu30,-x thin films on GaAs. Appl. Phys. Lett. 60. 1753-1755. 2. Tseng. M. 2.. Jiang. W. N.,and Hu. E.L. (1994)Measurements and analysis of Hall effect of a two dimensional electron gas in the close proximity of a superconducting YBa2C90,-x film. 1. Appl. PhyS. 76,3562-3565. 3. Likhatev, K. K. and Scmenov, V. K. (1991) RSFQ LogiclMemory Family: A new Josephson-Junction Technology for Sub-Terahcrtz-Clock-FrequencyDigital System. IEEE Trans. Appl. Supercond. 1 31. Chang.
28.
4. Kroemer, H. and Hu. E. (1996)"Semiconducting and Superconducting Physics and Devices in the InAdAISb Materials System," in Nanorechnology, G. Timp. Ed.,New York. AIP Press. In the press. 5. Kroemer. H.. Nguyen. C., and Hu. E. L. (1994)Electronic Interactions at SuperconductorSemiconductor Interfaces, Solid-state Electron. 37, 1021- 1025. (Proc. MSS-6.Garmiscb Partenkirchcn. Germany, Aug. 1993). 6. Kroemf?f, H.,Nguyen, C.. Hu.E.L.. Yuh, E. L.. Thomas, M.,and Wong. K. C. (1994) QuasipYticle transport and induced superconductivity in InAs-A1Sb quantum wells with 2% electrodes. Physica B 203, 298-306.(Proc. NATO Advanced Research Workshop on Mesoscopic Superconductivity, Karlsruhe, 1994). 7. Feynman. R. P.. Leighton, R. B., and Sands, M.(1965) The Feynman Lectures on Physics; Vol. 3: Quantum Mechanics, Addison-Wesley, Reading. Sec Sec. 21-9. a. Kittel. €. (1986)Introduction ro Solid Stare Physics. Wiley. New York. 9. Tinkham. M.(1975)Introduction to Superconductivity. McGraw-Hill, New York. 10. de Gennes. P.G. (1966)Superconductivity ofMerals and Alloys, Benjamin, New York. 11. Likhanv. K. K. (1979)Superconducting weak links, Revs. Mod. Phys. 51, 101-158. 12. Andrew. A. F. (1964)The thermal conductivity of the intermediate state in superconductors, Sov. Phys. IETP 19,1228-I231. 13. van Houten, H.and Beenakker. C. W.J. (1991)Andreev reflection and the Josephson effect in a quantum point contact, fhysicu B 175,187-197. 14. Mead. C. A. and Spimr, W.0. (1964) F e d Level Position at Metal-Semiconductor Interfaces, Phys. Rev. 134.713-716. 15. Nakagawa, A., Kroemer, H.,and English. J. H. (1989) Electrical properties and band offsets of InAdAISb n-N isotypc heterojunctions grown on GaAs, Appl. Phys. Len. 54. 1893-1895. 16. Silver, A. H..Chase. A. B., McColl, M.,and Millea M. F. (1978)Superconductor-Semiconductor Device Research, Funcre Trends in Superconductive Electronics. Charlottesville. VA. J. B. S.Dcaver. C. M. Falco. H.H. Harris,and S. A. Wolf, Eds., Am. Inst. Phys. Conf. Ser., vol. 44,Am. Inst. Physics, pp. 364-379. 17. Clark, T. D..Prance. R, J.. and Grassie. A. D. C. (1980)Feasibility of hybrid Josephson field effect transistors, 1.Appl. fhys. 51,2736-2743. 18. Takayanagi H..Alrazaki, T.. Nina. J., and Enold, T. (1995)Superconducting Three-Terminal Devices Usins an I n A s - B d Two-Dimensional Electron Gas,Ipn J. Appl. Phys. 34, 1391-1395. 19. Akazaki, T..Nina, J., and Takayanagi, H. (1995)Superconducting Junctions using a 2DEG in a Strained InAs Quantum Well Inserted into an InAlAsflnGaAs MD Structure, IEEE Tram. Applied Supercond. 5.2887-2891.
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352 Selected Works of Professor Herbert Kroemer
Reprinted from P. M Petroff, K. Ensslin, M. S. Miller, S. A. Chalmers, 11. Weman, J. L. Merz, H. Kroemer, and A. C. Gossard, "Novel Approaches in 2 and 3 Dimensional Confinement Structures: Processing and Properties," Superlattices and Microstructures, Vol. 8(1), pp. 35-39, 1990. Copyright 1990, with permission from Elsevier.
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Superlattices and Microstructures, Vol. 8, No. 1, 7990
NOVEL APPROACHES IN 2 AND 3 DIMENSIONAL CONFINEMENT STRUCTURES: PROCESSING AND PROPERTIES. P. M.Pemff, K.Ensslin. M.Miller, S. Chalmers. H. Weman, J. M m , H. Kroemer and A. C. Gossard Materials Department and Elecaical and Computer Department, University of California. Santa Barbara.CA. 93106 (Received 30 July 1990)
In this paper we review two novel types of quantum structures. The first, a i d at producing during growth quantum wire superlattices relies on the deposition of tilted supcrlatticcs. Some of the difficulties associated with the growth of tilted supcrlattices and the novel supentine superlattice have been discussed and solutions proposed. The sbcond type of quantum s t r u c m aimed at producing zero dimensional confinement SIXWXWCS relies on the formation of an antidot lattice. The transport properties of antidot lattices with various pericdicities axt presented. 1) Intrcduction The present interest in nanostructures and quantum structures properties has led to the development of sophisticated and novel processing and testing procedures. Depending on wether mesoscopic or true quantum structures are desired, the processing requirements differ drastically. Indeed, the mesoscopic regime requires only devices with dimensions smaller than the coherence length of the carriers. This regime for high quality 111-V compounds semiconductors requires devices with sizes larger than a few lOOOA. Recessing such devices is rather easily done with standard lithography techniques (electrons. X-rays and UV lithography). To exhibit easily detectable quantum confinement effects, two and three dimensional carrier confinement structures must have sizes below 5mA. Confinement effects have been demonstrated [ 1-81 in structures with larger dimensions, however the ~ small and the properties are confining potentials a r always detectable only at low temperatures. The proper choice of semiconductors will rclax the dimensional requirCmenrs [8] but the available systems are few. In all cases, the lithography techniques have been stretched to their limits and because lithography methods are used, the quantum structures density is small. In this paper, we report on recent progress achieved in the processing of quantum wire superlattices using the tilted superlattice (TSL) structures and a novel type of superlattice, the "Serpentine superlattice". The second half of the paper describes recent advances in antidots structures processing using the focused ion beam. The optical properties of quantum wire superlattices and the transpo~ properties of antidot stn~ctumare presented.
2) Advances in Direct Growth of Quantum Wire Superlattices The process relies on the fabrication of Tilted Superlattices (TSL) which offer the possibility of tilting the superlattice periodicity axis at any angle with the substrate [9.10]. The quantum wire superlattice consists of a thin TSL layer sandwiched by two layers of wider band gap material.
07~9-6O36/90/0~0035 -k 05 $02.0010
The TSL is fabricated by alternate deposition of fractional monolayers of two 111-V compounds on a vicinaly orientcd substrate. First demonstratcd for the GaAs-AlGaAs system, TSL structures have also been demonstrated for the GaSbAlGaSb system [ll]. The method allows for TSL whose periodicity is function of the substrate misorientation angle and of the TSL tilt angle B, with respect to the terraces normal. The TSL periodicity for a given substrate misorientation angle, 0:can be continuously tuned by changing the tilt parameter p. The TSL period is given by:
T=
Pd
[ tan2a+ (1 - p)']K The fraction of monolayers for the two semiconductors are m and n and the tilt parameter is -+n. The step height 6 for GaAs is 2.83A. The 3 difficulties associntcd in the TSL deposition arc: a) the requirement of a periodic step array over the entire substrate, during the deposition of the TSL as well as the deposition of the buffer layer and the cladding layers requircd for the fabrication of a quantum w i superlattice. ~ b) the requirements of a uniform tilt angle of the TSL over the entire wafer. c) the necessity of maintaining sharp interfaces between the quantum wires and the cladding layers. We examine subsequently the recent progress made in solving these 3 problems. A) Step Ordering on a Vicinal Semiconductor Surface
The vicinal surface as delivered by the manufacturer has a man misorientation a,which does not cornspond to the presence of a periodic step array on the surface. A Gaussian distribution of terraces with a mean dimension I=d/tga is present on the surface. Fortunately, for the GaAs [12] and GaSb [ll] (100) substrates, nature provides us with a self correcting process which allows us to obtain a periodic step lattice out of a gaussian distribution of steps around a mean misorientation a.If a potential banier to
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Superlattices and Microstructures. Voi, 8. No. 1, 7990
I
Figure 1: Schematic of two misoriented surfaces with a m d a n step m y (A) and a paiodic w m y (B). atomic motion prevents atoms from going down from one terrace to the other, e.g. from 1 to 2 or 2 to 3 (Figure I), bcfon it is incorporated at the step as part of the growing layer, an equalization of the terrace length takes place providing that a layer growth regime is established. This effect was demonstrated analytically and by Monte Carlo simulations 1131. The existence of a potential banicr to atom motim from one tancc to the other is found to be necessary to the elf canxting process. The origin of this potential barrier is not clear, however one might speculate that the bond breaking mechanism is more difficult if hybridized beads an formed at step ed es and more bonds k v e to te M e n if the a t o m goes one terrace to motha. Intuitively, the short t c m e , e.g. 2 in Figure 1, will w l a W y faga than the larger adjacent one, e.g. 3 in igun 1, since the number of atoms impinging on tcrrace3islarga. The preparation of the vicinal surface is done by obsaving d w g growrh of a buffer h y a , the double peak smcture of the specular beam in the RHEED pattern when the incident electron beam is orthogonal to the step edges.
L
0
25 50 j5 TSL composition (%AIAs)
100
Figure 2: Phase diagram of TSL growth surface morphology as a function of substrate temperature and AiAs compositionobtained fromthe RHEEDdata analysis. MEE deposition. Data points represent smooth growth. Lightly shaded area represents regions where growth is mostly smooth but appreciable island nucleation is taking place on the tmaces. Heavily shaded area represents rough growth ~ 4 1 .
bm
Fp"
~efullwidthathalfmaximumisdircctlycorrclavdtothe step periodicity and the distance between these peaks is dated to the viciial surface misorientation. The proper umditioas [14] for producing a paiodic m y of steps will depMd m the sllrfacecompositioa,thcgrowthtempuatuIe T and wctha gmwlhis taking place in the molecular beam epitax W E ) or the migntion enhanced epitaxy (MEE)
ikl
&
For MXGa1.,As system grown in the ME.E mode, a phase diagnm has bcM established experimentally [14] as a function ofx and T. As shown in Figm 2 for a AsKia flux mi0 of 6. thtre is no idul &-position condition that will presave steps for a GaAs-ALAS surface during MEE deposition of a TSL. However. a GaAs-A1xGal.xAs TSL can be grown while preserving a good step structure at a rcmpeianrn T*6oo'cfor x4.5. Thc prrsavationofa step lattia at lower temperarures T 1T indicate a periodicityial/B.lllUSthe . tance fluctuations c a r c d p d to the well know=ov de Haas (SdH) aclll.aooa The curierdensity f o r b various garc bias arc dcdpced fnnn the w M(uurcMnts 8s well as the SdH minima position& Similar resulta arc obtained for antidot snuuuru in the high mobility sample after an illumination
. .
P*.
Ibeminiown in h a t low magnetic field is assumed to careopond to electron delocahtion when the diameter of the t+omn orbits is smaller than the spacing between
two an-
The anti& sizt isconmkdby the size of its associated depletion layer which is assumed to be a
B (T)
Figure 6: Longitudinal maghetoresistance versus magnetic field at 4'K for an antidot lattice with a periodicity prMonrn The gate bias voltages are also indicated. cylinder. An upper limit for the depletion layer length Qepl of the carriers is given by b p i . = p/2-&. The diameter of the cyclotron orbit, 2& corn ndin to the minimum in pxx is given by 2&=(2nNS)ghlxe%,. Bm is the field comsponding to the minimum in the magnetoresistance.
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Superlattices and Microstructures, Vol. 8, No. I, 1990
acknowltdgc financial support by the AH%R ud QUEST, a National Science Foundation Science and Technology ccnttr. Refatnces:
2
3
5
4
N, (10"
6
7
an-')
Figure 7: Mobility versus carrier density for the antidot latdce in the low mobility sample. The canier density was changed by applying a gate bias. A striking ConSeQuence of the effective screening of the antidot potential by the 2 DEG is the depletion layer n the antidot periodicity. We have observed periodicities lead to a more effective screening and therefore smaller depletion layer. The d c s t depletion la dimension was about ~ O O for A a periodicity of 2000j(cr This leads to the possibility of p d w i n g rntidotlatliccs with c x a m l y small pcriodicities providing the focused ion beam probe size can be reduced below its present value (sooA). The mobility in these antidot lattices varies greatly with their periodicity. As shown in Figure 7, for the same value of Ns,the antidot lattice acts as a scattering center array. This was clearly rcvcBcd by the absence of mobility changes (N,=constant) due to illumination of the antidot lattice in the low mobility sample.
$S?ZKx
4) Conclusions
In this paper we have reviewed two novel types of quantum structures. The first aimed at producing during growth quannun Win superlatticesd i e s on the deposition of tilted superlattices. Some of the difficulties associated with the p w t h of tilted superlatticcs have been discussed and solutions proposed. The serpentine superlattice strucnrr~which offm the possibility of producing quantum wire stNctum has been presented. The second type of quantum structure^ aimed at producing zero dimensional confinement structures relies on the formation of an antidot lattice. The transport propcrtics of antidot lattices with various puiodicities have been discussed. A delocalization regime in the magnetoresistance corresponding to a transition to a classical 2 DEG transport has been observed as a function of the applied magnetic field. Acknowledgements-It is a pleasure to thank Y.T. Lu and H. Metiu for the modeling of the crystal growth and J. English for his valuable help with the MBE growth. We
B.J.vanWees. H.VanHouten, C.W.Beenakker. J.G.Williamson, L.P.Kouwenhoven, D.van der Marel. and C.T.Foxton, Physical Review Letters 60. 848 (1988). T.J.Thomton, M.Peppcr. H.Ahmed. D.An&ews. and G.J.Davies, Physical Review Letters 56, 1198, (1986). Ch.S&orki and U.Mcrkt. Physical Review letters 62,2164 (1989). M.A.Reed. J.N.Randal1, R.J.Aggmal, R.J.Matyi, T.M.Moore, and A.E.Wctsc1, Physical Review 60, 535 (1988). T.P.Smith 111. K.Y.Lee, C.M.Knoedler. J.M.Hong, and D.P.Kern. Physical Review B38, 2172 (1988). T.Hiramoto. K.Hirakawa and T.Ikoma, Joumal of Vacuum Science and Technolorn B6.1014 (1988). Y.Hirayama, T.Saku, and Y.Borikoshi, Physical Review B39, 5535 (1989). W.Hansen. M.Horst. J.P.Kotthaus, U.Merkt, Ch.Sikorski and K.Plooe. . Phvsical Review Letters 58, 2586 (1987). J.M.Gaines, P.M.Peuoff, H.Kroemer. R.J.Simes, R.S.Geels and J.H.English, Joumal of Vacuum Science and Technology B6,1378 (1988). P.M.Peuoff, J.M.Gaincs, M.Tsuchiya, R.Simes, L.A.Coldrcn, H.Krocmer, J.H.English, and A.C.Gossard. Journal of Crystal Growth 95, 260 (1989). S.A.Chalmers, A.C.Gossard and H.Kroemer. Applied Physical Letters (submitted 1990). S.A.Chalmers, A.C.Gossard. P.M.Petroff, J.Gaines, and H.Krocmer, Journal of Vacuum Science and Technology B7.1357 (1990). H-G.Gossmann. S.W.Siden, and L.C.Feldman, Joumal of Applied Physics 67,745 (1990). S.A.Chalmers, A.C.Gossard, P.M.Petroff, and H.Kroemer, Journal of Vacuum Science and Technology B8.431 (1990). Y.Horikoshi and M.Kawashima, Journal of Crystal Growth 95, 17 (1989). M.L.Miller, H.Wehman, L.Somoska, C.Rior, H.Kroemer , and P.M.Petroff, International Conference of Physics Semiconductors Rocctdings (Submitted Thessaloniki 1990). H.Wehman, M.Miller, J.Merz and P.M.Peuoff, Materials Research Society Proceedings (submitted 1990). Y.T.Lu, P.M.Petroff and H.Metiu. Applied Physical Letters (submitted). M.Tsuchiya, P.M.Petroff, and L.A.Coldren, Applied Physical Letters 54, 1690 (1989). K.Ensslin and P.M.Petroff, Physical Review B41, 12307 (1990). F.Laruelle, A.Bagchi, M.Tsuchiya, J.Merz and P.M.Petroff, Applied Physical Letters 56, 1561 I
(1990).
358 Selected Works of Professor Herbert Kroemer
..When you look at the history of technology, you see that the principal applications do not evolve Incrementally, but are created by the technology. Until you come up with such applications, you cannot judge how promising the technology is. I t is utterly foolish to ask immediately what a new technology is good for." Herbert Kroemer
Reprinted with permission from
H. Kroemer,"Heterostructures Tomorrow: From Physics to Moore's Law," Inst. Phys. Conf. Ser., Vol. 166, pp. 1-11, 1999. Copyright 1999, IOP Publishing Limited, UK.
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HeterostructuresTomorrow: From Physics to Moore’s Law Herbert Kroemer ECE Department, University of California Santa Barbara, CA, USA 9310*
Abstract Research on heterostructures with below-2D dimensionality is predicted to be the most challenging research area in heterostructures for the next few decades. The central problem will be the suppression of statistical fluctuations in size, shape, and placement of these structures. Large progress may be expected, but specific results are almost impossible to predict.
1 ) Introduction Heterostructures used to meun compound semiconductors. Today, compound semiconductors means heterostructures [ l l , Even studies of bulk properties nowadays are ultimately undertaken because the materials and properties studied are important for heterostructures (HSs). Anyone having any doubt about this is invited to consider what would be left of compound semiconductor research and technology in the absence of HSs-and whether this symposium would even exist. In fact, HSs are assuming a n increasing role even for Si devices. Nothing illustrates the importance of HSs better than the award of the 1998 Nobel Prize in Physics for the discovery and understanding of the Fractional Quantum Hall Effect (FQHE) in a HS-confined quantized quasi-2-dimensional electron gas (BDEG), following the 1982 prize for the discovery of the uordinary”(= integer) Quantum Hall Effect (first seen in the 2DEG at a Si/SiOe interface in what were basically MOSFET structures). The FQHE also illustrates another point that is central to my presentation: The futility of making long-term technological predictions. The FQHE discovery was completely unexpected, and the history of semiconductor technology is in fact littered with unexpected discoveries. As a result, much of the history of long-term technology forecasts has been a history of failures-the longer the forecast period, the larger the failure [21, because the larger will then be the impact of new discoveries that could not be taken into account a t the time the predictions were made. I believe that this unpredictability is a characteristic of all really big research breakthroughs. In fact, I shall refrain from making predictions of
* Electronic mail:
[email protected] 359
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specific research results; all I shall attempt is to predict research directions for, say, the next decade or so, not their results. Some people might argue that my critique of predictability may apply to future research breakthroughs, but that it should be possible to predict the applications of already ongoing research. I believe that this is a fallacy, too, and I will, in fact devote the last section of my presentation to this point.
For now, let us take today’s BDEG as our point of departure for looking at “tomorrow.” The quantized BDEG was a first case of a successful structure with reduced dimensionality. Much of today’s quantized-HS research is concerned with reducing the dimensionality of the electron system further, from 2-D quantum wells (with one direction of quantization) to 1-D quantum wires (two directions of quantization), and ultimately to 0-D quantum dots, with all threc directions quantized. This trend brings altogether new promises-and problems. Although nonquantized HS devices have by no means disappeared (for example, they form the basis of HBTs), I shall concentrate here on these newer quantized structures, with emphasis on the most extreme case, 0-D quantum dots. This is where I see the most challenging research problems for the “tomorrow”in the title of my contribution.
2) The 2-D Electron Gas-A
Review
A 2DEG is more than just a thin 3-D electron gas; the term refers to a gas in a narrow HS potential well for which the electron motion perpendicular to the plane of the well has become quantized t o the point that there is no longer any transverse motion across the well. For simplicity, consider a quantum well of width w with infinitely high walls. Its n-th transverse state (ignoring the unquantized motion along the well) has the confinement energy
where m* is the electron effective mass. Assuming, for example, w = lOnm and m* = O.lm,, we obtain an energy level separation between the two lowest states of 3E1 = 113meV, which is large compared to kT even at room temperature, and much more so at lower temperatures. Actual quantum wells do not have infinitely high walls, and hence have lower energy level separations. But energy level separations large compared to kT are readily achievable, for sufficiently narrow wells even at room temperature. At sufficiently low electron concentrations, only the lowest subband will then be occupied. According to the laws of quantum mechanics, any current ucross the well requires a superposition of at least two different transverse quantum states with different confinement energy, and if only the lowest state is occupied, all transverse motion is suppressed, even though the wave function still extends over the full width of the well. In this way we obtain a quasi-two-dimensional electron gas, the “quasi”
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alluding to the fact that the wave functions are still in 3-D; only the current is restricted to the plane of the well, without any lateral excursions even within the well. The high mobilities in such wells that formed the basis for the QHEfractional or otherwise-are achieved by applying the trick of modulation doping, a core ingredient of today’s HS technology. It is this modulationdoped BDEG that has dominated the physics research on heterostructures during the last two decades. As we shall see shortly, the transverse quantization is also a key ingredient on today’s quantum well lasers.
3) Quantum Wires: Ultra-High Mobilities? The first impetus for a further reduction in dimensionality was probably Sakaki’s work in which it was pointed out that a 1-D electron gas could, in principle, exhibit vastly larger mobilities than even a modulation-doped 2DEG [31.The central idea was the following. Mobilities are limited by the rate with which electrons can lose their momentum in the current flow direction by scattering events. In a BDEG, just as in 3-D, this loss of forward velocity can be accomplished by a series of small-angle scattering events within the plane of the quantum well; there is no particular scattering bottleneck. The transition from 2-D to 1-D is a much more drastic step in the basic physics than the step from 3-D to 2-D. In a lDEG, there are no longer any energetically accessible states with a sideways momentum, and the scattering physics changes dramatically. The mobility-limiting scattering process is now pure backward scattering, in which the electron must completely reverse its direction of motion in a single scattering event. For quantum wires with the relatively high electron concentrations that would be of practical interest, these scattering events involve a relatively large change in the wave vector k of the electron. But such processes tend to be relatively inefficient, hence the prediction of huge mobilities, which would be of obvious device interest-if the quantum wires were otherwise ideal. Unfortunately, a new scattering process now rears its ugly head: Quantum wires have a large surface-to-volume ratio, and interface roughness scattering (IFRS) at the seemingly inevitable atomic-scale irregularities in the electron confinement potential now tends to limit the mobility. In principle, IFRS plays already a role in narrow quantum wells. But it is possible to reduce the atomic roughness a t planar heterointerface to a very low level: Atomically flat quantum wells, grown over islands with a useful area, are in principle achievable, and have in fact been achieved, a t least for selected crystallographic orientations. But the problem of reducing irregularities a t the hetero-interfaces of a wire structure is vastly more difficult: Here, imperfections in lithographic dimensions inevitably enter the problem. With the help of several clever techniques, impressive progress has been made, but Sakaki’s original goal has remained elusive. The reason I bring all of this up here is to illustrate a key point that will dominate much of the rest of my presentation:
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With the transition from 2-D to 1-D and below, the interface irregularity problem becomes THE fundamental obstacle to the realization of the theoretical promise of structures with reduced dimensionality. As we shall see, this is true not only for electron transport structures, but for photonic structures as well. 4) Going to the Limit: Quantum Dots
As I said earlier, much of today’s research is concerned with reducing the dimensionality of the electron system further, from 2-D quantum wells to 1-D quantum wires, and ultimately to 0-D quantum dots, all with dimensions sufficiently small to lead to quantum effects in all confinement dimensions. These developments are what I think of foremost when I think of “heterostructures tomorrow.” What are the motivations for this trend, other than pure curiosity? One of the key points is the dimensionality-dependence of energy level distribution. 4.1) Density of States Distributions
The simplest representation of the static energy level distribution is in terms of the density ofstates (DOS) of the structure, defined as the number of states per unit energy interval, as a function of the energy at which a narrow energy interval is centered. This density of states is fundamen tally different for different dimensionality of the electron system, as illustrated in Fig. 1. It is a standard textbook fact that for a 3-dimensional gas of free electrons, the DOS increases monotonically and continuously with energy; more specifically, it is proportional to the square root of the electron kinetic energy:
Here m* is again the effective mass of the electrons, and the energy is measured from the bottom of the conduction band (for holes downward from the top of the valence band). For a BDEG, the lowest subband has a constant energy density,
provided the total electron energy & exceeds the energy &1 is of the lowest transverse bound state in the well. Higher subbands obey a law just like (3), but with a different starting energy, leading to an overall staircase distribution as shown. So long as the Ferini level stays below the bottom of the second subband, we have a quasi-2DEG, the case of greatest
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fundamental interest (at least to us). Note the discontinuous jump from zero t o a constant value, especially of the lowest subband, in contrast to the continuous increase in D in the 3-D case. As we shall see, this jump has important beneficial consequences for QW lasers.
e
E
0 3
D1
DO
Fig. 1. Density of states for simple systems with dimensionality decreasing from 3-D (a)to 0-D (d). For (b) through (d) only the lowest two subbands are shown. The really big transition in the physics occurs again when we go from a 2-D gas to a 1-D quantum wire, with two quantized dimensions. In the ideal "textbook" limit, the density of states now jumps to infinity a t the bottom of each 1-D subband, falling off with increasing energy according to the inverse-square-root law for the n-th subband
where & .is the energy of the bottom of the subband. Note that, although
D, goes to infinity, the square-root singularity remains integrable. The ultimate limit of quantization is the zero-dimensional quantum dot, in which all three dimensions are quantized, leading to density of states distribution in the form of a string of delta functions, at the energy levels of the bound states of the confining box. 4.2) Laser Implications
Nowhere is the density-of-states distribution more important than in semiconductor lasers. Consider first the 3-D case. If we plot, not the density of all states, but only that of occupied states, we obtain a distribution with a peak somewhere above the minimum allowed energy. The electrons with an energy in the vicinity of that peak (and the holes around an equivalent energy peak) dominate the stimulated emission; there simply are not enough electrons a t lower energy to provide enough gain. But the energy of that peak depends both on the amount of population inversion, and-worse-on the temperature. This implies an
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6 undesirably large temperature dependence of the laser wavelength (and other laser properties). In a true BDEG, because of the abrupt jump of the density of states from zero to a finite value, the maximum density of occupied states always coincides with the bottom of the lowest 2-Dband, regardless of everything else. While this does not eliminate undesirable temperature dependences, it greatly reduces them. In fact, essentially all of today’s practical semiconductor laser diodes are based on quantum wells, for this reason as well as others (of lesser interest to us here). The situation evidently becomes even better for the sharply peaked distribution of the density of states in quantum wires (Fig. lc), and the delta function-like distribution for quantum dots (Fig. Id) would evidently be ideal. The trouble with this idea is that, for a useful dot laser, we need a very large number of participating dots, just like a conventional laser needs a large number of participating atoms or molecules. But while atoms of a given species are naturally identical, technology-dependent dots inevitably exhibit statistical fluctuations in their size and shape, with the result that the sharp delta-function distribution of Fig. I d becomes strongly broadened, each dot contributing a slice of the overall broadened distribution. (Similar problems arise already in arrays of quantum wires.) At any given laser wavelength only a fraction of the dots can participate, the rest “just sit there.” This is not a total disaster: If the electron-hole pairs in the non-participating dots would not undergo spontaneous emission or radiationless recombination, their presence would be of limited consequence. Unfortunately, significant inefficiencies are all but inevitable. Despite the latter, very impressive results with such lasers have been reported -including at this symposium-especially for multimode power lasers driven suficiently hard to swamp the loss processes. But there can be no doubt that a more perfect control over the dot size and shape remains a central research goal-probably the central research goal- the solution of which is essential if the full potential of the reduced dimensionality is to be realized. As a glance a t the program of this symposium shows, this is a key research topic already, and I predict that it will remain so for the “tomorrow” in the title of my presentation. 4.3) The Size/Shape/Placement Problem
Better control over dot size (and shape) will almost certainly require a regular dot placement into a periodic lattice. The approach of random nucleation of “self-organizing” dots on an unstructured substrate is not likely to lead to the size (and shape) uniformity ultimately required. This need for controlled placement will become particularly important if we want to make individual electrical contact to each dot in future electronic circuits, for which we will need a technology that automatically creates a regular array of dots, initially a periodic lattice of dots a t predetermined locations, later extending to non-periodic controlled arrays.
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7 One approach towards this goal would be “smart substrates”, with lithographically pre-defined dot positions. However, even a predetermination of the dot positions does not necessarily lead to a uniform dot size when the dots become small. Consider a scenario in which, during MBE growth, all the atoms landing in a lithographically defined target area coalesce into a single dot at some pre-defined location within the target. If the atoms arrive in an uncorrelated beam, the number per target will be Poisson-distributed, that is, for dots containing an average of N atoms (or formula units, like Ga-As), the resulting dot sizes will fluctuate with a standard deviation of dN. For example, dots with an average size of 1000 atoms will fluctuate by about 3%,which for many applications will be too much. To achieve the desired sub-Poisson “squeezed” distributions calls for more sophisticated approaches than the “hit-and-stick” technique of MBE growth on top of a pre-existing lithographic pattern. I suspect that chemical vapor phase epitaxy offers a better chance of uniformity, but my own favored approach would be to first grow an unpatterned continuous layer of atomically-controlled thickness, and t o pattern this layer afterwards into dots of lithographically-defined size and shape. This, of course, calls for the development of suitable nanoscale lithography, but this is a something we will need anyway. 5) Coupled Quantum Dots as Future Electronic Circuits An altogether new field opens up when we consider quantum dots that are weakly coupled, for example by tunneling between adjacent dots. Controlling the tunneling by suitable gate electrodes offers a new kind of active electronic circuits that operate on the single-electron level. This is already an active research field [4], and I predict that it will become one of the most important areas within tomorrow’s heterostructure research.
5.1) Charge Quantization and Single-ElectronDevices Charge is rigidly quantized. Yet, because the charge quantum is so small, all of today’s devices treat the electronic charge as a continuous fluid. If anything, charge quantization is considered a nuisance, because it causes shot noise. Yet, from the fundamental perspective, charge quantization could be the ultimate digital property in future nanoscale circuits. Consider a small heterostructure capacitor with a “plate” area L2, and a plate separation L. Ignoring edge effects, this capacitor has a capacitance C = EL, where E is the permittivity of the “dielectric.” To change the number of electrons on the plates by one electron, requires a voltage change AV=q&JL.
For a “nano-capacitor” with, say, L = 10nm and E = lo&,, we obtain AV = 181 mV, a value sufficiently large to permit, at least in principle, the control of the number of electrons on the single-electron level, with a
(5)
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8 tolerable noise margin. Conversely, the voltage appearing across the capacitor will be a measure of the exact number of electrons on the plates. An especially interesting phenomenon takes place when, in a string of weakly coupled identical capacitors an applied voltage is exactly halfway between two values corresponding to two exact integer numbers of electrons. The charge on the plates can then fluctuate, which implies a relatively free current flow along the string a t this voltage, but not a t other voltages, a phenomenon referred to as Coulomb Blockade, and playing a central role in ideas for future nanoscale circuits.
All of this requires-of course-that the capacitors in such a circuit have a sufficiently well-controlled value. Thus we are back to the problem of precise size control. But to achieve tight control over a capacitance is probably less difficult than to achieve similarly precise control over more size- and shape-dependent properties. All that is needed is control over the capacitor area; the exact plate shape does not matter, in contrast to the energy levels inside quantum dots, which are significantly shapedependent. Nor do we have to worry about interface roughness scattering: Capacitance is a purely static property. The real problem is that of statistical spatial charge fluctuations of the semiconductor background [41, but this appears solvable. It is considerations such as these that make me expect such devices to have a promising future. Because of the minimal currents flowing, and the presumably small voltages involved, single-electron circuits would meet another desirable goal: A low dissipation. 6.2) Stacked Quantum Dots as Modulated Quantum Wires.
One potential form of coupled quantum dots that intrigues me personally is that of a vertical periodic stack of identical dots, coupled to each other. In effect, such a stack would recresent a true one-dimensional conductor, but with the addition of a periodic potential along the conductor. As a result, the 1-D band structure would break up into alternating allowed and bands and forbidden gaps, a situation similar to what we all have seen in our textbooks, but technologically undoable until now. The transport properties in such a mini-band structure could be extremely interesting, including such possibilities as Bloch oscillations and negative differential mobilities a t high fields.
6) Will Quantum Devices Extend Moore’s Law? Much of the semiconductor community has developed an obsession with Moore’s Law, that is, the observation that, for more than three decades, the dimensions of devices have shrunk exponentially, thereby making possible chips with an exponentially increasing number of devices. This process must of course saturate somewhere, and at least for the last ten years, there have been regular predictions that this saturation is imminent-only to be regularly surpassed by actual continued progress. As a result one now sometimes sees Moore’s law viewed as if it were a law of nature, which somehow must continue to be valid until we reach atomic
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9 device dimensions, and our job is simply to find out what makes it continue to be valid. This is of course nonsense, but it has had a pernicious effect on the nonSi community: the over-selling quantized HSs as the magic ingredient that takes over when CMOS “runs out of technology.” The argument runs roughly as follows. If continued, the reduced device scales must eventually lead to structures that obey quantized transport laws rather than the drift-and-diffusion laws of mainstream Si devices. Now HS-based quantum devices are of course devices of this kind. By a leap of faith, much of the current research on HS-based quantum devices is therefore sometimes justified as research towards this post-Si era of devices. I wished it were so! I am not going to claim that this hope is without some rational basis. But if we are serious about it, we must pay more attention t o another problem: Moore’s law is ultimately a law of the exponential increase with time in the number of devices processed per processing step. The reduction of device dimensions was necessary to make this possible, but it was not by itself sufficient. Yet almost all current work on quantum devices is using serial manufacturing, one device at a time. That is fine for physics research. But if HS-based quantum devices with nanoscale dimensions are to fulfill the post-Si promises often made for them, we must pay more attention to the development of massively parallel assembly techniques that go far beyond ‘Y2K” Si technology. In fact, a look at present-day oneat-a-time quantum devices shows that the overall device dimensions are actually larger than the overall dimensions of present-day CMOS ICs, not to mention readily foreseeable CMOS dimensions a few years down the road. I do not say that it cannot be done; I am simply trying to draw attention to this need, and I do predict that work along this direction will play an increasing role. In fact, I consider the situation far from hopeless, and I cannot resist the temptation to speculate which directions this research might take. The Silicon Road Map seems to place its bets on two technologies: (a) Going to even shorter wavelengths in optical projection lithography [51, and (b) a form of e-beam projection lithography know as SCALPEL (= Scattering with Angular Limitation Projection Electron-beam Lithography) IS],which is a parallel rather than serial process I suspect that going to shorterwavelength UV is not going to go far enough to carry us to the dimensions of ultimate interest. SCALPEL looks more promising, but my personal suspicion is something altogether different: Abandoningprojection lithography altogether and going to nano-scale contact printing techniques that have recently shown remarkable promise I71.
7 ) So what will be the Applications? Let me now return to a claim that I made in the Introduction, about the futility of predicting applications. Whenever we work on exotic newphysics device structures with an uncertain future, we are almost
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invariably pressured into stating their practical applications-inevitably meaning applications within a few years. This is a worldwide problem, and it has been getting out of hand in recent years. The honest answer would be t o reply that we don’t know, and that it is in fact one of the objectives of the research itself to look into what applications that research might have. But the temptation is to justify our research by making speculative promises-which may or may not be realistic, and which at best will be realized only after a much longer time than the questioners expect. Such promises tend to diminish our credibility and may ultimately backfire in the fonn of diminished research support. We must fight this nonsgnse on a sounder basis. Ultimately, the justification of more open-ended research lies in its historical record, expressed by what I have once called the Lemma of New Technology [81: The principal applications of any sufficiently new and innovative technology always have been-and will continue to be-applications created by that technology. But this means that is fundamentally wrong to evaluate the promise of newly emerging dramatically different technologies by asking what their applications might be. Worse, an insistence on such “visible” applications tends t o suppress rather than advance progress. The future will belong to those who do not restrict theniselves in this narrow-minded way! One manifestation of this shortsightedness that we must fight particularly, is the cry for “more relevance” in university research, a cry that might be safely translated into a call for less open-ended research. But university research plays a central role in the education of the top technological leaders of the next generation. Restricting that research to what outsiders consider relevant simply deprives our students of acquiring an education preparing thein for the future-to the detriment of society as well.
References
For a recent review of driving forces behind these developments, see H. Kroemer, “Band Offsets and Chemical Bonding: The Basis for Heterostructure Applications,” Physica Scripta, vol. T68, pp. 10-16, 1996. A n elaboration on this point can be found in: H. Kroemer, “Devices for the Future: A Peek into the Next Century,” Int. Conf: on Solid State Devices and Materials, Yokohama, Japan, 1994, pp. 397-399 (Extended Abstracts).
H. Sakaki, “Scattering suppression and high-mobility effect of sizequantized electrons in ultrafine semiconductor wire structures,” Jpn. J. Appl. Phys., V O ~ .19, pp. L735-L738, 1980. For a recent review, see K. K. Likharev, “Physics and Possible Applications of Single-Electron Devices,” .Future EZectron Dev. J., vol. 6, Supplement 1,pp. 5-14,1995.
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151 For a recent review, see N. Harned, “Ultralight lithography,” IEEE
Spectrum, vol. 36, pp. 35-40, 1999. [61 See, for example, L. R. Harriott, “A new role for e-beam: Electron projection,” IEEE Spectrum, vol. 36, pp. 41-45, 1999. [71 S. Y. Chou, “Sub-lO nm imprint lithography and applications,”J. Vac. Sci. Technol. B , vol. 15, pp. 2897-2904, 1997. 181 H. Kroemer, “All that Glitters isn’t Silicon - or ‘Steel and Aluminum Re-Visited‘,”NATO Adv. Res. Workshop “Future fiends in Microelectronics: Reflections on the Road to Nanotechnology”, Ile de Bendor, France, 1995, S. Luryi, J. Xu,and A. Zaslavsky, Eds., NATO AS1 Series; Series E: Applied Sciences, vol. 323, Kluwer Academic Publishers, pp. 1-12.
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Nano-whatever: Do w e redly know where w e are heading?
.- W e rea//y don't know where we are heading". I believe that this is an extraordinary important field and one of the things, I believe is important, that we do not restrict our interest in this work to applications and that we do not l e t t h i s b e driven by perceived applications. If you look a t one of the things, I keep repeating is Kroemerls lemma of new technology. The principal applications of any sophisticated, new and innovative technology have always been and will continue to be applications created by that technology, rather than being pre-existing applications, where t h e new technology simply provided improvements.
I think this is exactly going t o be true in Nanotechnology. I think, we must follow t h e opportunities that the technology offers us and then see what applications might spread out.
Herbert Kroemer
Reprinted from
H. Kroemer, "Speculations about Future Directions," J. Cryst. Growth, Vol. 251, pp. 17-22,2003. Copyright 2003, with permission from Elsevier.
Herbert Kroemer on Nanotechnology 371 Available online at www.sciencedirect.com
JM~RNALwCRYSTAL GROWTH ELSEVIER
Journal of Crystal Growth 251 (2003) 17-22 www.elsevier.com/locate/jcrysgro
Speculations about future directions Herbert Kroemera.b9* Department. University 0.f California (UCSB). Santa Barbara, C A 93106, U S A bA4aterials Deparfmenl. University of California (UCSB). Santa Barbara, C A 93106, U S A a ECE
Abstract
Although MBE technology is over a quarter-century old, and has been outstandingly successful in the growth of semiconductor heterostructures, it has a large reserve of as-yet unexplored capabilities left, many of which are likely to play a role in the future evolution of MBE. Developments that can be anticipated are the additions of OMVPE techniques to MBE, for example, for gas etching and surface cleanup. A central problem will be finding MBEcompatible ways to achieve lateral pattern control down to the nanometer scale. Nanoimprint techniques are a good candidate for that. Self-assembled quantum dots will probably give way to lithographically defined quantum dots with much better control over size and placement. Heterostructures of materials other than semiconductors will be increasingly explored, like magnetic and superconducting structures, and may be even organics. 0 2002 Elsevier Science B.V. All rights reserved. PACS: 81.15.Hi; 81.16.-c; 85.30.-z; 85.35.-p
Keywords: A l , Nanostructures; A3. Molecular beam epitaxy; B3. Heterojunction semiconductor devices
1. Introduction Speculations about the future of technology are a hazardous business. Much of the history of longterm technology forecasts has been a history of failures, so I undertake the theme of my title with some trepidation. My only consolation is that I am sufficiently old that it is unlikely that I can be called to account for those of my speculations that will turn out to be wrong. But then, maybe some of them will turn out to be right. Let me start out by telling you what I d o not intend to talk about. I will not talk about the
growth of MBE as a production technology. Perhaps more importantly-and maybe more surprisingly-I will say almost nothing about the application of MBE to specific individual devices. One of my reasons for the second restraint is that others, more involved than myself, will present much of the future of specific devices at this conference anyway. But my reasoning goes beyond that-which leads me right to the heart of my intended topic. A study of the history of technology presents staggering evidence for what I have called, on other occasions, Kroemer’s Lemma of New Technology:
*Corresponding author. ECE Department, University of California (UCSB), Santa Barbara, CA 93106, USA. Tel.: + 1805-8933078; fax: + 1-805-8937990. E-mail address;
[email protected] (H. Kroemer).
The principal applications of any sufficiently new and innovative technology have always been-and will continue to be-applications created by that technology. [ I ]
0022-0248/03/$- see front matter 0 2002 Elsevier Science B.V. All rights reserved PII: s 0 0 2 2 0 2 4 8 ( 0 2 ) 0 2 1 9 9 - 1
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372 Selected Works of Professor Herbert Kroemer H. Kroemer I Journal of Crystal Growth 251 (2003) 17-22
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Now MBE is hardly a new technology anymore, but I am convinced that it has huge reserves left in itself, and that its future probably contains much more than we can currently predict. But if this is so, then we should not judge the future of MBE technology from the perspective of already-recognized applications, be they heterostructure lasers, HBTs, or what-have-you. Work on those amounts to simply doing something better than we can d o it already, but does not represent new applications yet to be created by MBE. I am the first to admit that this is a very speculative proposition, which will not be universally welcome, for two reasons: (a) Applications that will be generated by future MBE technology can, by their very nature, not be readily predicted; so I evidently talk about something that is anathema to any control-centered industrial manager. (b) Many of you-perhaps most-are doing MBE in an environment where you d o not have the ‘‘luxury’’ of doing MBE in a context of openended research, but are compelled to work on very specific applications. But this does not in any way diminish the usefulness4ven for those of you-of remaining aware of unanticipated things to come. And there are probably a few members of funding agencies in the audience, who should perhaps be reminded that the current obsession with so-called strategic research is little more than a fancysounding justification for the discouragement of open-ended research, even though the latter has historically been the ultimate source of most longterm progress. Nobody has said that better than Mermin in his delightful put-down:
I am awaiting the day when people remember the fact that discovery does not work by deciding what you want and then discovering it. [2]
point of view. A good point of departure is to compare MBE with OMVPE. To me, the two have more similarities than differences. Both produce carefully controlled high-quality epilayers from a stream of incident atoms or molecules. The principal applications of both are in growing heterostructure; “plain” non-hetero layers hardly deserve the elaborate equipment. Finally, both are ultimately technologies for chemical reaction synthesis, with the difference that in MBE the reactions take place only on the growth surface itself, while in OMVPE reactions in the gas phase play an important role. All differences arise from a difference in the mean free path of the molecules on their way from some source to the growth surface. In MBE, this path is large compared to the distance traveled, in OMVPE is short. This central difference gives each of the two techniques certain advantages and disadvantages relative to its competitor, and I believe the future development of both techniques will include attempts to minimize the disadvantages by incorporating some aspects of the “other” technique. Hence I anticipate future MBE equipment that contains, within the same envelope, an OMVPE capability. In fact, combining the two technologies-albeit not in a n integrated piece of equipment-is already being practiced: Some of my colleagues at UCSB working on the new nitrides have found it useful to grow structures where an OMVPE nucleation and template growth is followed by a n MBE growth. I expect that we will see more of this kind of hybrid growth, using whichever of the two technologies is better for whichever part of the overall structure. Finally, some indium compounds grow well under In-stabilized or even In-rich conditions, bordering on a new form of beam-fed liquid-phase epitaxy.
3. The lateral resolution problem 2. What is MBE?-a
broad generic view
My approach to the future of MBE calls for a rather broad generic view of MBE that may go beyond present-day realized capabilities, and before turning to specifics, let me explain this
MBE has been spectacularly successful in the degree of control and design freedom on the “vertical” scale along the growth direction, down to individual atomic monolayer control, but it lacks-in common with other crystal growth
Herbert Kroemer on Nanotechnology 373 H. Kroemer I Journal of Crystal Growth 251 (2003) 17-22
technologies-any significant lateral pattern control within those beautiful monolayer planes, especially on the sub-micron scale. These limitations have always been present; they will simply become more severe as we wish to grow increasingly sophisticated structures, especially if the sophistication calls for smaller lateral dimensions, which is likely to be the case. Hence, this can be readily predicted to be one of the dominant developments of the future. There are two separate aspects involved in this: Multi-step growth, and high-resolution lithography. Let me start with the former. 3.1. Multi-step interrupted-growth techniques
At present, we are still relying almost exclusively on post-growth conventional photolithography. Worse, we are relying on what I would like to call single-shot growth followed by lithography-based processing. By the latter I mean a single MBE growth sequence-no matter how complicated the internal layer structure-followed by one or more processing steps. What we really need is the capability to have multiple growth sequences separated by processing steps that take place outside the MBE chamber. In Si technology, this capability is routinely present; we would benefit from it, too. There has recently been some progress in this direction, often referred to as MBE “regrowth” techniques, where a second MBE growth follows some ex situ processing after a first growth. I predict that research in this direction will be one of the important research topics in the years to come. The problem with all such regrowth techniques is the introduction of interface contamination and defects at the restart interface, especially if ex situ chemical processing has taken place. Simply stopping GaAs MBE growth and exposing the surface to air, without doing anything else, introduces interface defect concentrations (in this case acceptors) exceeding 2 x 10’’ crnp2, with much higher concentrations on processed surfaces. There are of course applications where such defect concentrations are acceptable, for example, when the doping levels on both sides of the interface are
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sufficiently high to swamp the interface defects. But we do not want to be restricted to such cases; we want to be able to have “invisible” stop-andrestart interfaces, say, inside a laser structure. Protecting a GaAs surface during ex situ exposure with a film of As, a technique used successfully for GaAs surface studies, is not the answer for processing, because it protects only those parts of the exposed surface that are left alone during; it does nothing for a surface exposed during the processing, for example, by etching. More research on those interruption-induced defects is called for, along with the development of in situ cleaning techniques within the vacuum envelope. I doubt that “energetic” techniques, such as ordinary sputtering, e-beam bombardment, or ion-assisted etching will be a fully satisfactory answer: These techniques create damage; and while this damage may be acceptable in many structures, it will be unacceptable in others, and if we do not wish to limit ourselves in what we can do, we need some less-energetic techniques, presumably purely chemical or photo-chemical ones. This is an area where OMVPE has an advantage. Thermal gas etching is a standard part of OMVPE, and I anticipate that it will become more widely accepted in MBE, too. This will obviously not be done inside the UHV MBE growth chamber itself, but in an interlocked chamber for gas processing. Once we have “lost our innocence” by taking this step, I would not be surprised if we equip the gas chamber with a separate OMVPElike growth capability of its own. In fact, we might wish to mix MBE with OMVPE even for the growth itself, as is already done in some nitride technology. Once we have “benign” surface cleaning techniques, we will also increasingly employ pre-growth patterning technologies, including the patterned deposition of non-volatile metal precursors. Reawakening the old vapor-liquid-solid growth technique on a nanoscale appears a possibility. 3.2. Beyond optical lithography?
When discussing structuring on a nanometer scale, people often propose the use of AFM or
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STM tips as quasi-lithographic tools for achieving the desired resolution (and precise placement). The trouble with such probe methods is that they are serial, that is, one object at a time. This is fine for building physics research structures that require just a handful of devices, but it is far too slow for structures on the level of complexity as today’s integrated circuits. The same comment remains largely true even for serial electron beam writing, except for relatively simple structures. Those who dream about extending Moore’s Law by such serial techniques might d o well to recognize that anything with less than lo9 devices per chip is just not interesting as a competition to CMOS, and then do their own throughput calculations-along with what this means for the equipment amortization cost per chip. For demanding applications involving a large production volume of structures with high complexity, a parallel assembly technique is absolutely required. In the last analysis, Moore’s Law is simply a statement about the triumph of parallel assembly via optical lithography with finer and finer resolution, which ultimately required shorter and shorter wavelengths. Current trends in mainstream IC technology are toward extreme-ultraviolet (EUV) lithography-at an astronomical equipment cost. Such costs may be economically acceptable in the IC industry with its huge production volume, but many of the applications of MBE are not of this kind. There is no doubt in my mind that we do wish to participate in the push towards nanoscale dimensions. But in this case we should expand our lithography horizons beyond optical lithography, and I d o not think that X-ray projection lithography is the answer. There has recently been a rapidly increasing interest in going back some 550 years to Gutenberg’s printing press, but on the nanometer scale (see, for example, Ref. [3]). While I am not persuaded that nanoimprinting will take over from EUV lithography in silicon IC technology, I believe that we should consider it as a natural partner of MBE. I can visualize the printing, not only of masks, but of growth precursors that subsequently react with incoming molecular (or atomic) beams.
4. On self-assembled quantum dots
One way around the lithography resolution problem is to work with nanoscale self-assembled quantum dots that form under certain conditions during MBE growth. I am very impressed by what has been achieved with this technology, for example, in the low-threshold laser field; I refer the reader to the numerous papers at this conference for details. But I believe that the approach of using spontaneously nucleated dots is ultimately too limited, or-to put it positivelyis only the proverbial tip of the iceberg of what might be achievable. If and when we achieve dots with a much better uniformity and with a tightly controlled placement, this will open up a much wider range of capabilities. Many of my QD friends consider 10% (linear) size fluctuations as excellent uniformity; but that means a 30% volume fluctuation, and 20% fluctuations in the quantum energies. There certainly are applications for which this is sufficient, like LEDs and lowthreshold lasers without tight spectral constraints, and possibly other devices, especially if the dots need not be electrically contacted individually. But I am convinced that the true potential of QDs will require us to d o much better. In order to achieve the kind of size uniformity that will ultimately be required, controlled placement will almost certainly be necessary-which calls for some sort of the pre-growth lithography to which I alluded earlier (maybe imprint-based). The sooner we start moving in that direction, the better it will be. And of course, we need not only dots, many applications will require interconnect lines. This calls not only for a nanoscale line technology, it also calls for a predictable placement of the things to be connected. Ultimately, we will almost certainly want to go to much smaller dots (and narrower lines) than what we are exploring today. At that point, statistical Poisson fluctuations will seriously enter the picture. Any technique that relies on simply collecting the atoms impinging over a certain target area will suffer from these. For example, a Poisson distribution with an average of 1000 atoms will have a standard deviation of k 3 3 atoms, or about 3%. At that point we will need
Herbert Kroemer on Nanotechnology 375 H. Kroemer I Journal of Crystal Growth 251 (2003) 17-22
growth techniques that are more deterministic in assembling the correct number of atoms. One obvious way of minimizing Poisson fluctuations would be to first grow extended layers of controlled thickness (something we know how to do very well) and then create the dots (and lines) by “cookie cutter” lithography with nanometer resolution. Furthermore, that continuous layer need not be the final material itself; it could be a precursor, for example, an In film, to be reacted with As after patterning. Regardless of details, nanometer lithography will again be required. I will probably be told by some that there are no applications for dots this small. That would almost certainly be true i f we restricted ourselves to the kind of applications that dominate the MBE usage of today. But remember what I said in the Introduction about new technology creating its own applications. I am convinced that this would be true again here.
5. Beyond “classical” semiconductors MBE, as a crystal growth technique, started with 111-V compounds, especially GaAs and (Al,Ga)As, and that continues to be its mainstream, although by now all 111-V compounds have been grown for one purpose or other, almost invariably in the form of heterostructures. The “hottest” 111-V materials are of course the nitrides. There has also been significant work on 11-VI compounds, but work on other materials is only now becoming a major part of MBE research and technology. The most active emerging class of new MBEgrown materials is that of magnetic materials, especially magnetic semiconductors. Much of that work sails under the flag of spintronics. Inasmuch as there are numerous papers on this topic at this conference, I will simply refer readers to those papers, and only express my expectation that these, and other magnetic materials will be an increasingly important application of MBE technology. What MBE technology, with its tightly controlled and highly instrumented growth procedures, can bring to bear on such materials is not simply an ability to grow thin films with-
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maybe-better quality. Instead, the emphasis will be on heterostructure involving layers of different materials; including heterostructures with nonmagnetic semiconductors. This is in fact a trend we see already. I am not persuaded that all the applications that have been predicted for spintronics are realistic. But this skepticism should under no circumstances be interpreted as a criticism of the research itself. I am guided here by my own Lemma of Technological Innovation, stated earlier, which suggests that this particular new technology, too, will create its own applications, which may or may not have anything to d o with the predictions made today. Another class of materials that I believe will play an important role in the future of MBE technology is that of high- T, superconductors, including superconductor-semiconductor hybrids. Much of my own research during the last 12 years has been on such hybrids, more specifically on socalled superconductive weak links in which an MBE-grown heavily modulation-doped InAs quantum well (with AlSb barriers) acts as a coupling link between two superconductor bodies (Nb) deposited on the InAs by ordinary sputtering [ S ] . The quality of the super-semiinterface has emerged to be crucial, and it would probably be beneficial if the superconductor, too, could be grown by MBE. Given this background, I hope I can be forgiven for saying a few words about the combination of MBE and superconductors. Some of the high-T, cuprates, especially YBCO ( = YBa2Cu307-x), have been prepared by MBE, but the cuprates are poor candidates for supersemi hybrids: They require deposition (or a postdeposition anneal) in a strongly oxidizing environment at high temperatures, a deadly combination for any classical semiconductor. Nor has the inverse approach of growing the semiconductor on top of the cuprate superconductor been more successful: The semiconductor tends to reduce the superconductor, which destroys the super-conductivity. Perhaps the most interesting (and challenging) superconductor candidate for MBE growth is the new intermetallic (non-oxide) superconductor magnesium diboride (MgBJ, with its remarkably high critical temperature (for a non-oxide) of 39K. Being non-oxidic, it might be compatible
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with semiconductors for future super-semi hybrids, an old favorite topic of mine. In fact, initial reports on the MBE growth of MgB2, at remarkably low growth temperatures (< 320°C) on various substrates, including specifically Si (1 1 l), look promising [j].Given the low growth temperatures, growth on 111-V compounds might be possible, including specifically on InAs, the ideal coupling medium for semiconductor-coupled superconductive weak links. Finally, I would not be surprised if MBE were applied to organic materials. The driving force to do so would be the tightly controlled and highly instrumented growth procedures of MBE, which
might offer capabilities beyond those of classical organic chemistry.
References H. Kroemer, Rev. Mod. Phys. 73 (2001) 783-793. [21 D. Mmnin, Phys. Today. 5 2 (1999) 11-13. [ 3 ] C. Kim, M. Shtein, S.R. Forrest, Appl. Phys. Lett. 80 (2002) 4051 (this paper contains extensive references to earlier work. See also a series of conference papers in J. Vac. Sci. Techno]. B 19 (2001) 2707). [41 M. Thomas, H.-R. Blank, K.C. Wong, H. Kroemer, E. Hu, Phys. Rev. B. 58 (1998) 11676. [5] K. Ueda, M. Naito, Appl. Phys. Lett. 79 (2001) 2046.
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